DEGREE PROJECT IN INFORMATION AND TECHNOLOGY, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019

Characterization of Passive in MultiBand FDD Systems

TOMÁS SOARES DA COSTA

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF AND COMPUTER SCIENCE

Characterization of Passive Intermodulation Distortion in MultiBand FDD Radio Systems

TOMAS´ SOARES DA COSTA

Stockholm September, 2019

Communication Systems School of Electrical Engineering and Computer Science Kungliga Tekniska H¨ogskolan

Supervisors: Adnan Kiayani, Ph.D. Department of Algorithm System Design, Ericsson AB Stockholm, Sweden

Claes Beckman, Ph.D., Professor Department of Wireless , Kungliga Tekniska H¨ogskolan Stockholm, Sweden

Examiner: Slimane Ben, Ph.D., Professor Department of Wireless Communications, Kungliga Tekniska H¨ogskolan Stockholm, Sweden

Opposition: Jo˜aoTorres, Information and Communication Technology, Kungliga Tekniska H¨ogskolan Stockholm, Sweden

Abstract

Intermodulation distortion (IMD) is a phenomenon that results in generation of spurious distortion when two or more signals of different pass through a nonlin- ear system. In general, IMD occurs in active circuits of a radio system, however, passive wireless components such as filters, transmission lines, connectors, antennas, attenuators etc., can also generate IMD particularly when transmit power is very high. The IMD in the latter case is referred to as passive intermodulation (PIM) distortion. With the continuing advancement of radio system coupled with the radio spectrum scarcity, PIM interference is recognized as a potential obstacle to achieving the full capacity of a radio network.

The assiduous enhancement of radio systems for faster data speeds and higher capacity further exacerbate the PIM interference problem. Features like carrier aggregation (CA) and multiple input multiple output (MIMO) make the PIM a more problematic issue. In modern co-sites, radio systems are often coupled together, operating in multiple bands. Furthermore, in division duplex (FDD) systems, transmitter (Tx) and receiver (Rx) operate simultaneously. In such scenarios, PIM is likely to occur in the ’s path and may potentially hit multiple Rx bands causing undesired interference.

The PIM sources in the BS radio systems can be divided into two groups, namely internal and external. Internal sources are the passive components within the radio such as filters, transmission lines, connectors, antennas, etc. External sources, on the other hand, are the passive elements beyond the BS but within the RF signal path such as metallic and rusty objects in antenna near field. For both types of sources, the high power current flowing through such passive objects can prompt a nonlinear behavior that in turn generates IMD.

This thesis addresses PIM distortion in multiband BS radio systems by devising a charac- terization. For this purpose, the research begins by establishing a mathematical model for IMD and reviewing the physics that prompt nonlinear behavior in these sources. Afterwards, the enhancements in radio systems that enlarge the bandwidths and ex- acerbate PIM are discussed. In particular, how IMD is worsen in broadband is

iii Abstract iv highlighted, and to complement this discussion, a review of PIM mitigation techniques is also presented. In the final part of this work, extensive lab measurement results are presented where effects of PIM with external PIM sources are analyzed and discussed. Overall, this thesis helps to build a better understanding of PIM interference problem in radio systems by providing useful insights into the nonlinear mechanisms in passive components causing PIM. Abstrakt

Harmonisk distorsion eller ”Intermodulationsdistorsion” (IMD) ¨arett fenomen som resulterar i generering av falska signaler n¨artv˚aeller flera radiosignaler med olika frekvenser blandas n¨arde passerar genom ett olinj¨artsystem. I allm¨anhetf¨orekommer IMD i aktiva kretsar i ett radiosystem. Emellertid, passiva tr˚adl¨osakomponenter s˚asom filter, transmissionsledningar, kontakter, antenner, d¨ampareetc., kan ocks˚agenerera IMD, s¨arskiltn¨ars¨andningseffekten¨armycket h¨og.IMD i det senare fallet kallas ”pas- siv intermodulationsdistorsion” (PIM). De senaste ˚arensutveckling av mer avancerade radiosystem, i kombination med radiospektrumbrist, har inneburit att PIM idag ses som ett av de st¨orstapotentiella hindren f¨oratt uppn˚aden fulla kapaciteten i tex 5G radion¨atverk.

Den st¨andigautvecklingen av de cellul¨araradiosystemen mot h¨ogredatahastigheter och h¨ogrekapacitet f¨orv¨arrarytterligare PIM-st¨orningsproblemet: Funktioner som b¨arv˚ags aggregering (carrier aggregation, CA) och ”multiple input multiple output” (MIMO) system g¨orPIM till ett ¨annu st¨orreproblem. I moderna samarbetsplatser, radiosystem ¨arofta kopplade ihop och fungerar i flera band.

I system med frekvensduplex (FDD-system), d¨ars¨andare(Tx) och mottagare (Rx) ar- betar samtidigt men p˚askilda frekvenser, kan PIM med h¨ogsannolikhet intr¨affai sig- nalenv¨agenoch dess distortionsprodukter potentiellt tr¨affaflera Rx-band och d¨armed orsakar o¨onskad st¨orning.

PIM-k¨allornai Basstationssystemen kan delas in i tv˚agrupper: interna och externa. Interna k¨allor¨arpassiva komponenter inne i radion s˚asomfilter, transmissionslinjer, kontakter, antenner etc. Externa k¨allor˚aandra sidan ¨arde passiva elementen bortom Basstations-antennen men inom RF-signalv¨agens˚asommetalliska och rostiga f¨orem˚ali antennen n¨arf¨alt. F¨orb˚adatyperna av k¨allor¨ardet den h¨ogaeffektt¨athetensom f˚ar s˚adanapassiva objekt att uppvisa ett elektriskt olinj¨arbeteende som i sin tur genererar IMD.

v Abstrakt vi

Denna avhandling behandlar PIM-distorsion i basstationssystem f¨ormultipla frekvens- band genom att utforma en karakt¨ariseringav de genererade signalerna. F¨ordetta ¨andam˚alb¨orjar studien med att skapa en matematisk modell f¨orIMD och sedan granska fysiken som skapar det olinj¨arabeteendet i olika PIM-k¨allor.

D¨arefterdiskuteras hur PIM genereras i bredbandiga radiosystem. I synnerhet diskuteras hur IMD f¨orv¨arrasi bredbandiga radiosystem samtidigt som en ¨oversikt av metoder att motverka dess effekter p˚aprestandan presenteras.

I den f¨orstadelen av denna rapport presenteras resultat fr˚anomfattande laborato- riem¨atningar,d¨areffekterna av PIM med externa PIM-k¨alloranalyseras och diskuteras. Sammantaget bidrar denna avhandling till att bygga en b¨attref¨orst˚aelseav PIM-st¨orningsproblem i radiosystem genom att tillhandah˚allaanv¨andbarinsikter om passiva icke-linj¨aramekanis- mer i komponenter som orsakar PIM. Acknowledgments

The research work reported in this thesis was carried out during the year 2019 at the Department of Algorithm System Design, Ericsson AB, Stockhom, and Department of Wireless Communications, Kungliga Tekniska H¨ogskolan (KTH), Stockholm, Sweden.

Foremost, I would like to express my sincere gratitude to my two supervisors Dr. Adnan Kiayani and Prof. Claes Beckman, who guided and helped me during the research of this thesis. I am deeply grateful to Dr. Adnan Kiayani for giving me the opportunity to work under his supervision during my time in Ericsson. His guidance and instigated in me work ethic, perfectionism and professional values that will support the remainder of my careers. I am also grateful to my supervisor at KTH, Prof. Claes Beckman, for the assiduous feedback and guidance. His tremendous amount of knowledge on the subject and positive attitude gave me the curiosity to further investigate the problem and were crucial during the research.

This thesis was financially supported by Ericsson AB, Sweden. Hence, I would like to express my appreciation to the company itself, the HR department for handling practical matters efficiently and everyone at the department of Algorithm System Design for creating such an inspiring work environment. In particular, I would like to express my gratitude to this department leader, Spendim Dalipi for giving me the opportunity to work in Ericsson, and for being a great person to work for.

I would like to thank my beloved friends in Portugal Pedro Croca, Pedro Martins, Ruben, Carlos, Nuno, Sebastiao, etc. for the experiences in the past five years. Without their constant support, motivation and company, this achievement would be nothing short than impossible. Also, I would like to extend the compliments to my peers, namely my friends Jo˜aoTorres and Mariana Filipe, who accompanied me during my time in Sweden and, with whom I had the pleasure to work throughout the academic year. Lastly, I would like to thanks the faculties and professors of both IST and KTH and, in particular, Prof. Jos´eSanta Rita for being my mentor and teaching me how to think.

vii Acknowledgments viii

I would like to extend my thanks to my beloved family as I would not be the person I am if not for them. Thanks my grandparents Rui, Dina, Fernando and Madalena, my cousins Andr´e,Teresa and Miguel, and aunt Margarida. Thanks to my dad, Pedro, thanks for inspiring me to become a engineer as well, for teaching me how to laugh and play sports, and for attending every event I ever participated, since the first day of school to the last soccer game. Thanks to my younger brother Martim, thanks for every fight, argument, game, holiday, birthday, moment I got to share with you, hopefully I will be able to repay your affection by becoming a great role model for you to follow and by help you with your endeavors. Lastly my thanks to my wonderful mother, Carla. You are my inspiration, and everything I ever accomplish or become is because of you.

Finally I would like to dedicate this work to the memory of my late aunt and uncle, Eug´eniaand Ac´acioBarreiros, who, unfortunately, will not be with me when I graduate. They were truly incredible persons whose memory I will forever cherish.

Stockholm, August 2019 Tom´asSoares da Costa Contents

Abstract iii

Abstrakt v

Acknowledgments vii

Contents ix

Abbreviations xi

1 Introduction 1 1.1 Background and Motivation ...... 1 1.2 Scope and Contributions of the Thesis ...... 3 1.3 Thesis Outline ...... 4

2 Fundamentals of Passive Intermodulation 5 2.1 Intermodulation Distortion ...... 5 2.2 Sources of Intermodulation Distortion ...... 8 2.2.1 Classification of PIM Sources ...... 9 2.3 Internal PIM sources ...... 11 2.3.1 Contact Nonlinearities ...... 11 2.3.1.1 Metal-Insulator-Metal situations in a RF system . . . . . 12 2.3.2 Electro-Thermal PIM Sources ...... 14 2.3.2.1 Electro-Thermal Theory ...... 15 2.3.2.2 Distributed PIM sources ...... 16 2.4 External PIM Sources ...... 17 2.4.1 Reflection on Metal Surfaces ...... 18 2.4.2 Dielectric Coating and Wave Polarization ...... 19 2.4.3 External Sources as PIM Antennas ...... 20 2.5 Discussion ...... 21

ix Contents x

3 PIM Distortion in Radio Systems 23 3.1 Evolution of Wireless Networks ...... 24 3.1.1 Overview of 3GPP Global System for Mobile Communications . . 24 3.1.2 Overview of 3GPP Long Term Evolution ...... 25 3.1.2.1 OFDMA and SC-FDMA Principles ...... 26 3.1.3 Overview of 3GPP Long Term Evolution-Advanced ...... 26 3.1.3.1 Carrier Aggregation Fundamentals ...... 28 3.1.4 Overview of 3GPP New Radio ...... 29 3.1.4.1 NR Physical Layer Principles ...... 30 3.2 Passive Intermodulation Distortion in Radio Systems ...... 31 3.2.1 Passive Intermodulation in Broadband Radio Systems ...... 32 3.2.2 Passive Intermodulation Impact on and Phys- ical Layer ...... 35 3.3 Passive Intermodulation Mitigation Techniques ...... 36 3.3.1 Physical Mitigation of Passive Intermodulation Interference . . . . 36 3.3.1.1 Guidelines for Mitigation of Internal Sources ...... 37 3.3.1.2 Guidelines for Mitigation of External Sources ...... 37 3.3.2 Radio Integrated Mitigation of Passive Intermodulation Interference 38 3.4 Discussion ...... 39

4 Measurements-based Analysis of External Passive Intermodulation 41 4.1 Radio Setup and Use Cases ...... 41 4.2 Power Analysis ...... 44 4.3 External PIM Analysis for Case Studies ...... 46 4.4 Digital Cancellation of PIM ...... 51 4.5 Discussion ...... 52

5 Conclusion and Future Work 55

Bibliography 59 Abbreviations

3GPP 3rd Generation Partnership Project 2G second generation 3G third generation 4G fourth generation 5G fifth generation BS base station BSS base station subsystem Bw bandwidth CA carrier aggregation CC component carrier CDMA code division multiple access CFO carrier frequency offset CM cubic metric CP cyclic prefix DFT discrete Fourier transform DL downlink ET electro-thermal FDD frequency division duplexing FDMA frequency division multiple access GPRS general packet radio service GSM global system for mobile communications HD distortion ICI intercarrier interference IDFT inverse discrete Fourier transform IEEE institute of electrical and engineers IM intermodulation IMD intermodulation distortion IM3 third-order intermodulation distortion product IMT International Mobile ISI inter symbol interference xi Abbreviations xii

ITU-R international union radio communication sector LS least squares LTE long term evolution LTE-A long term evolution advanced eMBB enhanced mobile broadband mMTC massive machine-type communications MCS metal clamp attached to small support structure MM metal-metal junction MIM metal-insulator-metal MIMO multiple input multiple output MSC mobile-services switching center NTL nonlinear transmission line NR new radio NNS network and switching subsystem OFDM orthogonal frequency division multiplexing OFDMA orthogonal frequency division multiple access OSS operation support subsystem PA power amplifier PAPR peak-to-average power ratio PIM passive intermodulation PIMP passive intermodulation products PHY physical layer PO physical PSD power spectral density PSK shift keying QAM quadrature QPSK quadrature phase shift keying RAN radio access network RB resource block RF Rx receiver RU radio unit SC-FDMA single carrier frequency division multiple access SER symbol error rate SNR signal-to- ratio SINR signal-to-interference plus noise ratio TDPO temperature coefficients of resistance TDPO time domain physical approach TDD time division duplexing Abbreviations xiii

TDMA time division multiple access Tx transmitter UE user equipment UL uplink UMTS universal mobile telecommunications system URLLC ultra-reliable low-latency communications WLAN wireless local area network WB wideband

Chapter 1

Introduction

1.1 Background and Motivation

Radio systems have experienced tremendous growth during the last few decades due to the ever-increasing demands of higher data rates, low latency, and better wireless con- nectivity. This is due to the growing data usage in mobile devices for modern services like multimedia contents, and the growing number of devices. Hence, existing wireless communication systems are specified to support the data rates within the range of 100 Mbps to 1 Gbps for both uplink (UL) and downlink (DL), depending on the mobility of the device. Currently, the 3rd Generation Partnership Project (3GPP) has defined standards for operators to accommodate data rates of 10+ Gbps during the radio trans- mission under various mobility conditions. In order to achieve even higher data rates, its required wider bandwidths and better flexibility in data transmission. However, the available bandwidth in radio-frequency (RF) spectrum is limited and, due to the numerous wireless services available, it is becoming completely saturated.

Given the restrictions of the spectrum and available technologies at the time of release, different generations of radio system have different operating strategies to provide in- creased data rates. Second generation (2G) radio systems, commonly referred as Global System for Mobile Communications (GSM), make use of narrowband Time Division Multiple Access (TDMA) techniques to transmit (Tx) signals. This technique increased the capacity of the radio system compared to the previous first generation (1G) tech- nology, as it allowed more users to be accommodated within the available transmission bandwidth. This technology uses 200 kHz wide RF channels and enables up to eight users to access each carrier, which results in data rates around 270 kbps. The next enhancement, third generation (3G) radio systems or Universal Mobile Telecommunica- tions System (UMTS), was introduced to increase this data rate. UMTS uses a wideband

1 Introduction 2

Code Division Multiple Access (CDMA) technology occupying a 5 MHz wide channel to transmit signals. In addition, this technology employs technologies like frequency division duplex (FDD) or time division duplex (TDD) to transmit data as well as Phase Shift Keying (PSK) modulation schemes to achieve data rates up to 2048 kbps. The next enhancement is the fourth generation (4G) also known as Long-Term Evolution which provides the aforementioned data rates of 100 Mbps to 1 Gbps. To realize such high data rates, this technology employs advanced techniques including new access schemes like Orthogonal Frequency Division Multiplexing (OFDM), higher modulation alphabets, advanced scheduling techniques, Multiple Input Multiple Output (MIMO) antenna con- figurations and Carrier Aggregation (CA) features to enlarge bandwidth. At the time of writing, the next radio enhancement, fifth generation (5G) or New Radio (NR) is on the brink of release. This technology will allow data rates of 20 Gbps in the DL and 10 Gbps in the UL per base station (BS) using adding techniques like mmW wave communications, i.e., utilizing available RF spectrum until 100 MHz, massive MIMO with beam-steering and dense network systems.

In achieving extremely high data rates, a big importance is placed on both user equip- ment (UE) and BS since they are expected to be multimode and multiband to support the transmission. However, there are restrictions on power consumption, cost and size, particularly on the UE side. The quality of the transmission is dependent on the sig- nal’s quality and elements of the radio system, hence interference problems must be minimized. Imperfections in the radio system architecture cause interference and arise due to the technical constraints of the components. This is especially problematic in BSs, where high amounts of current flow through the structure and affect the linearity of its components. In these high power systems, signal paths must be kept highly linear, or else imperfections start to arise given the nonlinear behavior. These nonlinearities can create imperfections in the system such as intermodulation distortion (IMD).

Intermodulation (IM) is a phenomenon that occurs when one or more transmit (Tx) signals with both one or more frequencies, or carriers, are input to a nonlinear system. The output produced are prejudicial spurious frequencies resulting from the combination of the input tones, i.e., prejudicial in-band and adjacent band frequency components are generated. These unwanted spectral emissions are called spurious emissions and can appear at the receiver (Rx) band causing interference to the desired receiver signal. If the nonlinear system that creates these new frequency components is a passive, linear element of these high power systems such as transmission lines, connectors, joints, etc. (internal source) or simply a metallic component in the RF path (external source), the phenomenon is called Passive Intermodulation distortion (PIM). The general topic of this thesis is the investigation of PIM in multiband FDD radio system. Introduction 3

1.2 Scope and Contributions of the Thesis

The goal of this thesis is to better characterize the PIM phenomenon in multiband radio systems. This characterization covers the basics of IMD, the underlying physics behind the nonlinear behavior of passive components that are prone to generate PIM when several Tx carriers flow through them, the exacerbation of the problem due to the enhancements of radio systems and corresponding mitigation techniques and, lastly, an analysis on external PIM given the measurements performed. While it is difficult to cover all the details associated with PIM in one thesis due to the complexity of the problem, the focus of the measurements is on external PIM since this part of the problem has been long overlooked.

The first contribution of this thesis is the extensive characterization of the PIM phe- nomenon made throughout the second and third chapter. Starting with the basics of the IMD to understand the concept, we then review the physics that trigger the nonlinear behavior in both types of PIM (internal and external), which generate the spurious spec- tral emissions. For internal sources, studies in the past decade, have concluded that one of the main contributors for this phenomenon is electro-thermal (ET) conductivity along with the mechanisms of electric tunneling in contact junctions. For external sources, the main contributor remains to be the phenomenon called the “Rusty Bolt” effect, however, PIM can still be generated of scattering in simple metallic sheets. Both of these are ex- plained by the same approach. Next, we review the enhancements of the radio system, highlighting key features that have exacerbated the PIM problem, particularly CA and increased complexity of BS. By using broader, modulated carriers instead of narrowband ones, the spectral regrowth is increased, worsening the interference issue. To finish this characterization, we review current PIM mitigation techniques used by manufacturers and operators. The strategy of physical techniques is to avoid the trigger of nonlinear behavior on passive sources whereas the strategy of the radio integrated techniques is to avoid PIM interference by relying on the mathematical model, e.g., frequency planning, lower Tx power, etc.

The second contribution of this thesis is the analysis of the measurements in the fourth chapter. The measurement setup emulates different real scenarios of external PIM. Inside an anechoic chamber a BS transmits a multicarrier signal towards several metallic objects placed within the RF path. By analyzing the power spectral density (PSD) of the PIM observed in each antenna element, we derived key observations regarding external PIM, especially the correlation of observed PIM power with the BS transmitter and PIM source. From these, it is possible to improve the understanding of external PIM, namely the physics involved in this scenario. Lastly, we review a digital PIM cancellation algorithm by applying one to the measurements. Introduction 4

1.3 Thesis Outline

Chapter 2 of this thesis gives a literature review of intermodulation distortion, internal and external PIM sources in radio systems, the physics of the nonlinear triggers behind PIM, and an understanding on how PIM is generated.

Chapter 3 of this thesis addresses the evolution of radio systems since the time where PIM first had its effect. In addition, it also accounts with the exacerbation of PIM generation in these modern radio systems due to the assiduous enhancements for increased data rates, especially the enlargement of bandwidth by CA and possible PIM sources in the transmission by the increase in BS complexity. Lastly, this discussion is complemented with an overview of existing PIM mitigation techniques used by manufacturers and operators, both physical and radio integrated.

Chapter 4 of this thesis investigates the relation between observed PIM power in the Rx, possible external PIM sources, and Tx. This is done by assessing PIM power on the antenna elements, namely by analyzing PIM’s PSD on antenna’s polarization. This analysis is based on the contents reviewed in the previous chapters. Lastly, a PIM cancellation algorithm (radio integrated mitigation technique) is implemented in the results to assess its performance.

Chapter 5 contains a summary of the work performed, the results obtained, and the significant outcomes from this thesis work. Chapter 2

Fundamentals of Passive Intermodulation

In any RF communication system, an ideal behavior is strived for, which translates into components with linear relation. Unfortunately, it is unavoidable due to the presence of weak intrinsic nonlinearities. Such nonlinearities result in interference problems, or intermodulation and harmonic distortion. Intermodulation occurs when an input signal composed of a sum of frequencies passes through a nonlinear system, generating new frequency content. The mixing of the fundamental frequencies creates new frequency components that are integer multiples of the frequencies of the input signal [1, 2, 3]. IM content appears both above and below the fundamental frequencies in the spectrum, and occurs in both active and passive “circuits”. An active circuit is driven by a (voltage) source whereas passive circuit does not require power. For instance, an active circuit can be the output stage of an amplifier, mixers, etc. A passive circuit on the other hand could be an RF connector, antenna element, a metal sheet, etc [2, 4, 5, 6]. In this thesis, the focus is on IMD caused by passive sources, and its implications on radio system per- formance. However, we first briefly review the fundamental of passive intermodulation distortion in this chapter. Thus, in the following section, the mathematical formulation of the IMD is presented, which is followed by a review of the physics behind the most common PIM sources, e.g., triggering mechanisms.

2.1 Intermodulation Distortion

Intermodulation becomes an interference problem when, in the RF spectrum, the IM frequencies generated by the circuits fall into the receiver bands near the transmitter signals. To develop a mathematical model of IMD, consider a simplified case where our

5 Fundamentals of Passive Intermodulation 6

input signal denoted here as Vi , is composed of two tones with frequencies f1 and f2, with corresponding of A1 and A2, which can be written as

Vi(s) = A1 cos(2πf1t) + A2 cos(2πf2t). (2.1)

This signal then passes through a non-ideal and, therefore, nonlinear current-voltage (I-V) system, whose is represented by a nth-order power series with coefficients K1,K2,K3, ... The output signal of the nonlinear system, denoted as Vo, can be described as

2 3 Vo(s) = K1Vi + K2Vi + K3Vi + .... (2.2)

Note that, in the series (2.2), the larger the K − th coefficient, the more dominant is the nonlinear term, i.e., the bigger the nonlinear contribution. Upon combining both equa- tions and expanding the series terms using the trigonometry identity and the Binomial theorem, additional terms at new frequencies are generated [4, 5, 7]. These spurious fre- quency components are either (multiples) of the original signal or the result of the sum or difference of the original signals frequencies. These additions and subtrac- tions of the original frequencies f1 and f2 are named IM products, or frequencies, that follow the relationship,

fIM = nf1 ± mf2, (2.3) where n and m are integer coefficients. The sum of the absolute value of these coefficients rd provides the order of the IM product. For instance, 2f1 ± f2 are 3 order IM products th (|2| + |±1| = 3), 3f1 ± 2f2 are 5 order IM products and so on. Despite some of the higher and lower products being easily filtered out, odd order IM frequencies are of most concern since they are typically located close to the original signals (if the original frequencies in the original signal are close, which is common for multicarrier signals). An example of an output spectrum showing the full extent of this phenomenon in frequency is displayed in Figure 2.1. In general, the proposed concept can be extended to multiple frequency components, for example, in the case of three frequency components mixing in a nonlinear system, the corresponding third-order IM products (IM3) would be f1 ± f2 ± f3.

In case the signals are modulated, the bandwidth (Bw) of the IM products created must be considered, not just the center frequency. The bandwidth of the IM products is wider than the original signals bandwidth, and scales with the order of IM. For instance, if both Fundamentals of Passive Intermodulation 7

f1 f2 2 1 -f +f 2 1 f f 2 1 -f -f 1 2 2f 2f 1 2 1 2 f1 2f 2f 1 -2f -2f 2 Non-linear 1 2 1 -2f 2 -f -f 1 2 3f 3f 2f 2 1 3f Function 3f -3f -3f 1 f2 2 4f 4f

DC Tx1 Tx2 f

Fig. 2.1: Intermodulation frequency spectrum input signals are 1 MHz wide, the third-order product will have a 3 MHz bandwidth, the fifth-order product will have a 5 MHz bandwidth, and so on [6]. So, it is possible to conclude that, if both original signals have the same bandwidth then the IM product bandwidth is the original signal bandwidth multiplied with the IM product order number [3]. Likewise, for different bandwidth modulated signals, the IM products bandwidth derives from equation (2.4) [4]

BwIM = |n|Bw1 + |m|Bw2. (2.4)

Another important consideration of the IM products is the respective amplitudes. IM products have small amplitudes if the input power on the signals is low, however, if the input power is high (which is the case in radio systems) the amplitudes will also increase. From mathematical expressions developed in [4, 5, 7], if we increase the input signals such that the desired output power is increased by 1 dB, the IM3 product amplitude increases by 3 dB. In theory, the relation between fundamental signal power and the IMD distortion components power is directly proportional, with the slope being the product order number. However, in practice, the power level of the measured IM products are lower than the theory as proved in [7, 8, 9]. Figure 2.2 shows the theoretical and realistic plots for output IM3 product signal. It also shows intersection of the theoretical line extension of output IM3 signal and the desired output power ratio, or the third order intercept (TOI) point. This is the point where the power growth of the intermodulation product intersects, or is equal to, the output power growth of the fundamental signal [10, 11, 12]. In general, the output power of the intermodulation intersect point (OIP) can be calculated according to the equation:

OIPN = Pout + |IMN /(N − 1)| , (2.5) Fundamentals of Passive Intermodulation 8

IP2

IP3 (dB) out P

1:1 3:1 2:1

Pin (dB)

Fig. 2.2: Representation of intersection points (IP) of the 2nd and 3rd order IM prod- ucts with the desired output power, red, green, and blue respectively. The dashed lines represent the theoretical slope from the calculation whereas the full line represent the actual plot.

where Pout is the output power of the fundamental signal, N is the order of the product, and IMN is the level (in dBc) of the intermodulation product relative to the fundamental.

By solving the previous equation in order to IMN and obtaining the distortion values, it is possible to determine the amplitudes for each IM product. Higher-order terms have lines with a sharper slope meaning their amplitude variation will be higher, however, they are restrained due to a lower OIP and spread over a larger bandwidth. Thus, in addition with the mathematical expansion previously mentioned, we denote that the amplitude of each order IM is lower than the order before, i.e., 5th order IM products have lower amplitude than 3rd order IM products, 7th order IM products have lower amplitude than 5th, and so on. Nevertheless, the increase in input power leads to higher IM products which may block desired Rx signals.

In conclusion, IMD is a phenomenon characterized by the transmitted signals that are mixed in the nonlinear device, e.g., respective carrier frequencies, bandwidth and power. This new frequency content, or IM products, are characterized by the same parameters. However, the impact of the distortion is also dependent on the Rx characteristics like sensitivity level of the radio systems.

2.2 Sources of Intermodulation Distortion

As mentioned in the beginning of the Chapter, IMD is the result of two or more sig- nals interacting in a nonlinear device to produce unwanted signals. This mainly occurs Fundamentals of Passive Intermodulation 9 in active circuits (devices) such as amplifiers and mixers. In a radio system, nonlin- earity of the power amplifier (PA) has the most significant impact on the transmitter output spectrum. The relative strength of these spurious IMD products can be very strong. In active components such as the PA, intermodulation can be more predictable. This is mainly due to existing models based on measurements taken from specific PA [13, 14, 15]. The nonlinearities from the PA derive from a phenomenon called compression. It occurs when increasing the input power in the amplifier does not result in the corresponding increase in the output power when operating near the maximum power. Generally, nonlinearity from active devices can be predicted, and there is already some extensive research on how to model these type of nonlinearities. [3, 4, 16]

To a lesser extent, IMD can occur in passive circuits, e.g., passive devices or compo- nents. PIM distortion classifies the effects of the unwanted IM products generated by the nonlinear properties of a passive component in a radio communication system. As stated before, these products may lead to interference in the receiver bands of several RF systems since they can likely obstruct a channel, also leading to a reduction in channel’s signal to noise ratio [1, 3, 4]. In general, the occurrence of the nonlinearities associated with the passive components are hard to predict, and the strength of the products de- pends on the strength of the nonlinear relation. However, there is extensive research on the mechanisms that generate the nonlinear behavior. Thus, it is possible to distinguish different types of PIM sources based on the nonlinear triggering mechanisms. In the following section, we classify the different types of existing PIM sources that are capable of producing IM products, or PIMP.

2.2.1 Classification of PIM Sources

PIM has been known as a potential interference source in radio communications systems for a long time, with first studies dating back to 1989-90 [5, 17]. However, due to the adoption of wideband multicarriers signals and increasing saturation of the frequency spectrum, PIM problem has started to regain considerable interest in recent years. In general, PIM distortion can be classified into three distinct types: design PIM, assembly PIM and rusty bolt PIM, [18]. This characterization is based on different types of nonlinear trigger mechanisms that generate PIM interference which, in turn, can require a different solution.

Design PIM refers to the choices taken by designers when choosing the layout members, in other words, picking components based on trade-offs of size, power, rejection and PIM performance. Assembly PIM designates the interference created by the degradation of the installed system over time, based on the quality (materials, robustness, stability, interface) of the components and surrounding environment. Rusty bolt PIM is associated Fundamentals of Passive Intermodulation 10 with reflections of the downlink frequencies towards the uplink in metallic objects (rusty fence, barn, etc.) in the beam’s propagation path. Essentially, any interference signals that can couple into the and has significant power than the desired received signal can lead to receiver desensitization. [18]

Based on the short description of PIM above, it is beneficial to, from now on, classify PIM sources into two types, internal and external. Internal PIM couples design and assembly PIM sources like coaxial cables, connectors, , antennas, filters, etc. [5, 6, 17, 19, 20]. External PIM refers to sources beyond the antenna such as support structures, tower and masts, wire fences and nearby metallic objects that re-radiate the prejudicial spurious emission towards the Rx. [5, 6, 18]

The signals mixing in a nonlinear passive source normally come from transmitters shar- ing an antenna structure or nearby towers with conflicting antenna patterns. Some of the triggers that derive the nonlinear I-V relation in the passive components to generate the mixing of the frequency are damaged or poorly torqued RF connections, contami- nation (oxide, dirt, etc.), fatigue breaks, cold solder joints, electro-thermal conductivity, metallic material and corrosion. These mechanisms are all inherent to components of the radio system BS, e.g., internal sources. Each component has its own method to generate PIM. These methods described here are unavoidable, especially PIM due to ferromagnetic and ferrimagnetic materials since they are widely used in infrastructures and microwave components like isolators, circulators, , etc. [1, 6, 7, 21, 22]

In addition to these potential sources, nearby metallic objects are prone to generate PIM as well. Commonly seen in rusty metallic objects, PIM generation in external sources is commonly associated to the “Rusty Bolt” effect. However, it can still occur by scattering of the surface of external metallic objects. These sources are located beyond the antenna, typically in a site. For instance, sheet metal roof vents, loose cable hangers behind the antenna, overlapping layers of metal flashing are some of the possible existing objects that can radiate IM products back into the antenna. Also, depending on the site configuration, there can be multiple external PIM sources radiating simultaneously, both in front of and behind the antenna. [23, 24, 25]

On the upcoming sections, the physics of the generating mechanisms for the two possible type of sources, internal and external, are described in Section 2.3 and Section 2.4, respectively. Fundamentals of Passive Intermodulation 11

2.3 Internal PIM sources

In this section we discuss the physics of the triggers of the nonlinear behavior account- able for PIM generation in internal sources. Since most of these processes can arise from the same source, it is difficult to establish which one is the dominant during the PIM generation process. This is mainly due to the variety of models that exist to describe the different triggers, and the impossibility to concretely assess in a real ap- plication. Currently, it is known that several physical mechanisms are responsible for generating PIMP, namely, electron tunneling and thin dielectric layers between metallic contacts, micro discharge between microcrakcs and across voids (multipactor discharge), nonlinearities associated with dirt and metal particles on metal surfaces, high current densities, nonlinear resistivity of materials used, nonlinear hysteresis (memory effects) due to ferromagnetic and ferrimagnetic materials, electro-thermal (ET) conductivity ef- fects and poor workmanship that causes loose connections, cracks and oxidization at joints, [1, 5, 17, 21, 26].

Until recent studies, [1, 27, 28, 29, 30, 31], contact mechanisms in RF components were considered the main source of internal PIM in radio system elements such as filter, antennas, connectors etc. However, ET research surfaced and classified itself as another important contributor for PIM generation in internal sources. To a lesser extent, dirt particles and corrosion (contamination) still remain as a severe source of PIM and it is a compulsory problem to deal with in radio systems. Since the physics of contact mechanisms explain why corrosion can also generate PIM, the explanation of the triggers will focus on contact mechanisms and ET. This explanation will also play an integral role when assessing the results derived from the measurements in Chapter 4.

2.3.1 Contact Nonlinearities

As stated previously, one of the main mechanisms responsible for PIMP generation are the nonlinearities involved in metal contacts. Two physical contact situations can oc- cur, the metal-insulator-metal (MIM) situation and the metal-metal (MM) situation. Each of these physical structures, MIM and MM contacts, have several of their own distinct nonlinear mechanisms. MIM structures are more susceptible to electron tunnel- ing ,thermionic emission and corona discharge. MM structures, on the other hand, can create like junctions due to differences in metal work functions as well as nonlinear contact resistances due to thermal processes such as expansion and thermal variation [1, 21]. These two contact types may occur by a multitude of ways, especially since they are dependent on both ends of the contacts topography and pressure. Fundamentals of Passive Intermodulation 12

In general, it is impossible to achieve a full smooth surface on the termination of radio components during their fabrication process. When coupling two radio components, at a microscopic level, both contact surface topographies possess numerous peaks in random positions and a native oxide or sulfide layer covering it. The thickness of this layer depends on the chosen metals, and is usually in the order of couple nanometers [32]. Therefore, contacting two surfaces of this nature is comparable to contacting needle of various lengths [1, 21]. From this observations, one can assume that the “real” contact area is merely a fraction of macroscopic contact and, it is only happening in peaks making contact. Likewise, due to surface imperfections, the MM situations only occur at the microasperities where the mechanical pressure was strong enough to force the junction of the peaks. The analogous MIM situation occurs in case that the mechanical pressure is insufficient to pierce through the thin dielectric layer covering the metal’s surface [1, 21, 32]. Hence, due to surfaces topology, a contact can be seen as a combination of both types of structure. However, an increase in pressure translates into an increase in mechanical deformation, which enhances the size of the “real” area as it is forcing more microasperities connections, so it can determine whether MM occurs more often. Based on the factors that define the type of structure, e.g., deterioration, metals used and cleanliness, different models exist to describe the nonlinearities that appear [21, 32, 33].

Figure 2.3 shows the physical situation described above, where the current is constricted to flow through the microasperities. The determination of whether it is MM or a MIM scenario depends on whether there is a thin dielectric layer in between the microasper- ities, or appearance of corrosion in the void region. Nonetheless, the number of MM and MIM scenario depends on the amount of pressure applied. The PIM distortion generated at a junction can comprise of several contributions, either from MIM or MM, however some contributions are higher [1, 21, 32, 34]. In most radio systems, the applied pressure connecting two radio components can decrease, it is very likely that the main source for IMD occurs from MIM regions, especially since a high number of contacting zones can appear. In the following subsection, MIM situation is further explained.

2.3.1.1 Metal-Insulator-Metal situations in a RF system

The physic phenomenon responsible for the nonlinear behavior presented in MIM sit- uations is called tunneling theory as mentioned before. The general idea is that the current, or electrons, flow through a forbidden region between two propagating medi- ums. In MIM type of structures, the dielectric layer refers to this forbidden region and introduces a potential barrier that the electrons can not overcome unless the amplitude of the wave function (or current as called here) can exponentially decay to the other side of the barrier due to the transmission coefficient. The tunnel current between metals can Fundamentals of Passive Intermodulation 13

Metal

Air Regions Air Regions Air Regions

Metal

Fig. 2.3: Constriction of current in the connection between microasperities be obtained using the Simmon’s model, where the nonlinear I-V relations are portrayed. Given this nonlinear relation, IM products are generated. [1, 21, 32, 35]v

Besides electron tunneling, thermionic emission and corona discharge are another phe- nomenons that occur in MIM. In thermionic emissions, electrons jump the aforemen- tioned potential wall due to thermal energy. By doing so, a nonlinear current is generated that is dependent on barrier thickness. This current accumulates with the tunneling cur- rent but is typically weaker, therefore negligible. Although its current contribution is considerably less than the tunneling current, it is relevant to point that these weak non- linear currents can be accumulated at the interfaces. Corona discharge is a process that usually occurs in low pressure cases, i.e., when the junction start to loosen up. In this process the current flows from a high potential conductor (radio component) towards a neutral fluid, in our case, air [1, 32, 35]. In summary, one can deduce that the con- tribution for PIM distortion in contact situations can simultaneously be from multiple mechanisms.

In [34] and [36], the authors corroborated the relationship between contact mechanisms and nonlinear I-V equations. After deriving pressure-dependent nonlinear I-V equations for metallic contact interfaces and PIM models, the consequential PIM’s level can be obtained. It is dependent on contact resistance, surface current density and the nonlinear current coefficients. In other words, MIM contact structures can be seen as transmitters (Tx) of PIM signals, whose total power (in dBm) can be represented as

P [J(V )] P = 10 log int (dBm), (2.6) PIM 1 × 10−3 Fundamentals of Passive Intermodulation 14

where Pint[J(V )] is the total sum of the current generated by the several nonlinearities (transmitters) mechanisms of the contact. The mathematical approach of obtaining these currents is described in detail in [32].

There are several key conclusions that can be drawn from the discussion above. First of, as the mechanical load increases, the PIM level decreases much faster since the area of contact is dramatically increased. Hence, the thicker the dielectric layer in between contacts, the higher the PIM level. Secondly, for proper mechanical connections, i.e., no loose contacts, the cleanliness of the surface determines the PIM level. Based on these arguments, one can argue that the use of soft metals for contacts as the inherent coating and oxidation is thinner. Unfortunately, for this type of materials, there is the possibility that the deformation from the thermal increase of applying mechanical load permanently changes the surface’s original shape. This leads to a decrease in contact pressure when the contact temperature unavoidably decreases, which creates a gap between surfaces. As a consequence, inside the gap, dirt particles can intrude, creating undesired MIM PIM transmitters. Thus, the emphasis on cleaning and maintaining the radio system structure is enhanced.

In sum, PIM interference can be originated in contacts, mainly due to the ferromagnetic materials and dirtiness. These mechanisms are present throughout the RF network, beyond contacts and junctions, including transmission lines, resonant structures and antennas. Nonetheless, physical situation embedded in the radio system components generate PIM signals that can be accumulated throughout the system. These interfer- ences become more and more pronounced in high power BS radio systems, where the downlink signals contributing to PIM generation are substantially strong.

2.3.2 Electro-Thermal PIM Sources

In the previous subsection, we review how contact mechanism in BSs components can induce PIM interference. Additionally, these high power transmit signal can also produce electro-thermal effects which also induce PIM. The constant change in both thermal and electrical domain when modulated RF signals travel lead to time variant nonlinear conductivity, which is responsible for PIMP generation [1, 30]. As stated previously as well, PIM generation due to ET conductivity are also one of the main contributors to aggravate the problem in internal sources, so its physics are discussed in the following subsections. Fundamentals of Passive Intermodulation 15

2.3.2.1 Electro-Thermal Theory

In general, metals possess disturbing influences that impede the free flows of the electrons under a electric field, known as electrical resistance. According to the Wiedemann-Franz

Law, metals also exhibit a thermally-based resistance, Rth [37]. Therefore the specific resistivity of a material can be written according to a function of temperature (T ), expressed as equation (2.7) [1, 27, 30]

2 ρe(T ) = ρe0(1 + αT + βT + ...), (2.7)

where ρe0 is the static resistivity constant and α and β are temperature coefficients of resistance (TCR).

In a resistive element, the heat generated per unit volume, Q, is directly proportional to the current density, J. Thus, the electrical domain is coupled with the thermal domain according to equation (2.8)

2 Q = J ρe. (2.8)

The time needed to conduct the heat from the element to its surrounding environment at a given rate is captured by the thermal capacity Cv, and it is propelled by the heat conduction equation, given by equation (2.9) [1, 27, 30].

OT ∂T O · ( ) − Cv = Q. (2.9) Rth ∂t

Combining equations Equations (2.7) to (2.9), equation (2.10) is originated, which de- scribes a nonlinear system. This is a crucial result because it means that the electro- thermal process can be separated into static and dynamic components, with static and dynamic power signals Ps and Pd, respectively. They are dissipated through the respec- tive static and dynamic resistance components Rs and Rd, respectively. The total power dissipated over these resistive components is converted to the heat signal Q(Ps + Pd) and filtered by the material’s thermal response (baseband lowpass). This is relevant because, in a situation where two or more signals are applied to a resistive element (two-tone case), the instantaneous power of the signal varies periodically at the frequency of the two-tone input to the device. If the beat frequency is within the ther- mal bandwidth of the lowpass filter, periodic heating and cooling of the element occurs at baseband frequencies due to the oscillation of the instantaneous power. Consequently, Fundamentals of Passive Intermodulation 16 the resistance of the element varies periodically. This periodic oscillation creates a pas- sive mixer producing intermodulation distortion through up conversion (heterodyning) of the envelope frequencies at baseband to RF frequencies [1, 27, 30].

OT ∂T 2 2 O · ( ) − Cv = J ρe0(1 + αT + βT + ...) (2.10) Rth ∂t

The process described above is displayed in Figure 2.4. In sum, the electrical and ther- mal domain couple at RF frequencies due to low frequency variations in the dissipated electrical power. Note that the filtering property response (lowpass) of the thermal domain is due to the diffusive nature of heat conduction [1, 30, 31].

Thermal Response (f,T) I P

f1 f2 f (a)

IM products (f,T) O V

f1 f2 f (b)

Fig. 2.4: Passive mixing inherent in electrical and thermal coupling process: (a) input power spectrum Pi, resulting from two-tone excitation, interacting with the thermal response of the passive component, and (b) corresponding output spectrum voltages Vo after electro-thermal mixing has occurred

2.3.2.2 Distributed PIM sources

Passive nonlinearities in modern radio systems can be categorized in two main cate- gories, lumped, where PIM in generated by one main source, typically metal-to-metal contacts, and distributed, where the sources are scattered throughout the whole infras- tructure. Similar to the MIM scenario, in modern base stations, weak passive nonlinear- ities due to ET effects that act like PIM sources are spread throughout the system. The temperature’s dependence on conductivity produces appreciable electrical distortion in microwave elements as concluded in [1, 30]. So, due to electro-thermal effects previously explained in 2.3.2.1, distributed PIM distortion is typically modeled as a nonlinear trans- mission line (NTL). Note that this model can be used to describe PIM generation due to ET conductivity in passive components like coaxial cables and microstrips. These Fundamentals of Passive Intermodulation 17

Δt Δt z Δz Δz

E1 -E3 +E3 -E3 +E3 -E3 +E3 V(t,x)

z

Fig. 2.5: PIM’s signal strength sequential increase due to the generated fields in non linear consecutive points in the transmission line elements, alongside contact terminations (lumped components), play a major role on generating PIM in a radio system.

In the NTL model, the PIM distortion is generated by singular elements of a nonlinear transmission line. The sum of all the effect reproduced by the cells generate the total nth order PIM outage power due to ET effects. For a detailed explanation of how PIM is generated in each infinitesimal element, the reader is referred to [1, 29, 30]. However, to briefly summarize it, in a line component, a nonlinear electric field (E) of IM products is generated through the nonlinear current (J) produced by the varying heat dissipation (Q). The PIM signal is the sum of the electric fields accumulated throughout the line via different components. Basically, each line element functions as a nonlinear generator whose signal power depends on the element’s impedance (varies throughout the line). It is relevant to note that two electric fields are generated at each point, the forward one and the reverse. Yet, due to destructive interference after line’s length ∆z = λ/4, the latter one is negligible. However, PIM can still travel in the reverse way by reflecting the forward PIM signal at the line’s termination. In Figure 2.5, a representation of PIM generation from NTL model is displayed. In summary, one can deduce that the contribution for PIM distortion due to ET conductivity can be from the multiple resistive elements in which the current flows through.

With this, all main internal PIM sources in radio system components are accounted for. In the following section, we discuss the physics of external PIM sources to finalize the theoretical characterization of the phenomenon.

2.4 External PIM Sources

So far, the discussion has been focused on nonlinear triggers of internal PIM sources, however, the PIM problem goes beyond the internal constituents of a radio system. Fundamentals of Passive Intermodulation 18

PIM can also derive from unpredictable and uncontrollable external sources. In either case scenario, indoor or outdoor, solving the problems of site interference unveils the issues associated with external sources of PIM. In [23], the author performed a study regarding the challenges in a site. It concluded that potential non-linear objects such as sheet metal vents, metal flashing, ceiling tile frames, street lamps, etc. that are typically present in the RF path might generate IM products and re-radiate them into the system. As mentioned previously in 2.2, this effect is commonly referred to as the “Rusty Bolt” effect, demonstrated in [25]. Consequently, antenna location and orientation to remove external sources from the system’s RF path is extremely important. Antenna polarization also as an effect on how energy couples into the nonlinear object and how it is received back into the Rx. As shown also in [23], different antenna’s linear polarization (+45◦ and −45◦ respectively) lead to distinct levels of third order IM products generated externally by overlaying metal sheets.

In a typical FDD radio system, Tx and Rx functions are coupled into one antenna and, in a co-site scenario where multiple radios from the same or different operators are deployed, several antennas and bands act simultaneously. Distortion of the signals by intermodulation is a severe concern in site integration. PIM interference in the antennas is usually attributed to internal sources such as contact nonlinearities, explained and cited in 2.3.1 and 2.3.1.1, material nonlinearities, and electro-thermal nonlinearities [1, 5, 17, 20, 38, 39, 40]. However, as it was previously mentioned in section 2.2, PIM can be generated externally (beyond the base stations), in simple metallic components. Simple objects in the RF path like a rusty junctions or metal structures can either generate or reflect PIM products that are captured by the antenna as noise [5, 41, 42, 43]. The characterization of physics behind the triggering mechanisms of external PIM sources is explained in the following subsections.

2.4.1 Reflection on Metal Surfaces

As stated previously, metal flashing in the RF path can generate PIM. Not only this specific case, but for any finite metallic or dielectric component in the beam’s path. Although likely, a transient situation will not be considered for simplicity reasons. Con- sider the simple situation where a radio is transmitting towards a metal sheet, showcased in Figure 2.6. The incident wave reflects of nonlinear metallic surface. Consequentially, the scattered electric field by the surface can be calculated by the physical optics (PO) approach since it is a well-known and efficient method for high frequency diffraction techniques [44]. The PO approach abides that a local surface current is induced by the incident wave on the illuminated part of the body’s surface element. Consequently, an- other scattered field is created by summing the contributions of each lit element of the Fundamentals of Passive Intermodulation 19

Fig. 2.6: Two incident waves lit an area of the metallic surface (gray) and IM products are reflected of the nonlinear region generates given the mixing in the nonlinear region body’s surface by the induced current. For a perfectly conducting body, the postulated surface-current-density distribution in the frequency domain is given by the following equation [45, 46, 47, 48]

( −→ −→ −→ 2ˆn × H inc(R, ω) in the lit region J s = −→ (2.11) 0 otherwise

−→ −→ −→ wheren ˆ is the unit vector normal to the surface at point R, and H inc(R, ω) is the incident magnetic field with angular frequency ω.

In order to determine the reflected electric field, equation (2.11) domain needs to change from frequency to time. Afterwards, the sum of all contributions of the lit regions need to considered. This process is named Time Domain Physical Optics (TDPO) and is performed by the author in [46]. An application of this technique toward PIM problems was researched in [49]. By accounting for the induced nonlinear currents on metal surfaces, it is possible to calculate resulting scattered electric field. The frequency of the scattered field is of IM products. The paper also provides some nonlinear functions to properly simulate the electromagnetic considerations. The results presented in the publication validate the TDPO model, which explains the generation of PIM products of reflections on finite metallic surfaces. Yet, the complexity of the problem increases if it is considered dielectric coating and wave polarization. These variables are considered in the following subsection.

2.4.2 Dielectric Coating and Wave Polarization

In the previous section, the physics responsible for instigating electric fields of IM tones on conducting surfaces was developed. However, polarization dependence and dielectric Fundamentals of Passive Intermodulation 20 coatings were not incorporated into the discussion. Likewise, the purpose of this section is to deepen the study of PIM generation in external sources by assimilating these two variables. Scattering of a material coated body is a complex problem yet the physics approach for studying it remains the same, TDPO.

Even though the example displayed in Figure 2.6 was a simple planar conducting surface, the TDPO approximation technique remains valid for a convex surface coated with an absorbent dielectric material [46, 50, 51]. Hence, consider now a convex surface, coated with an absorbent dielectric material that causes an effect on the high frequency scattering fields due to the respective intrinsic properties (relative µ and ε). This urges repercussions in the diffraction phenomenons and surface impedance, Z. Hence, with a dielectric coating, the impedance of the object, Z, changes. This has an impact on the nonlinear current, J, produced by equation (2.11), namely the direction of which the current is produced and the strength of the current. [50, 51, 52]

Consider now the incidence angle, θi, and the incident wave polarization orientation, which can be either perpendicular (P⊥) or parallel (Pk). These affect the parameters that characterize optical phenomenons, namely, reflection coefficient, R. This correlation can be expressed as [51, 52]

Z − cos(Θi) Z − sec(Θi) Rk = and R⊥ = . (2.12) Z + cos(Θi) Z + sec(Θi)

These reflection coefficients have a direct affect on the magnetic field used in equation (2.11) and prove that, for different wave polarizations, different responses ought to be expected. Mainly because it directly affects the nonlinear current produced, J, and, consequently, the strength of the scattered electric field, E. This electric field radiated from the object has a random polarization, dependent on the current path. Using this formulation, in [52], the author calculated the reflected electric field of a dielectric surface for different polarizations.

In summary, both variables, dielectric coating and wave polarization, have an effect on the induced nonlinear current at the metallic object surface. This effect can be the a change on the radiated IM products amplitude, or an affect in the current’s direction, i.e., the polarization with which they are reflected.

2.4.3 External Sources as PIM Antennas

In the previous subsections, we discussed the physics behind IM generated products of reflections in metallic objects, which is based on the TDPO approach. Basically, it induces a nonlinear current which radiates an electric field with the frequency of IM Fundamentals of Passive Intermodulation 21 products back to the BS antenna, which can couple with the receiver chain. In fact, the TDPO approach is applicable to calculate the scattered EM fields of large reflector antennas and dielectric bodies. However, in the case of a reflector antenna such as a parabolic reflector, the main cause for the radiation of spurious signals is the electron tunneling in the MIM junctions when the parabolic reflector is illuminated by high power microwave radiation, i.e., the “Rusty Bolt” effect. In this case, nonlinear currents from two or more transmitters are induced in the reflector surface and flow through the object. During this process, the local current encounters connectors, slits or cracks that are seen as MM or MIM junctions. These give rise to nonlinear I-V characteristics that generate and radiate IM products through tunneling phenomena and corona discharge of the two or more currents flowing through the junction. The generated IM products are then radiated back at the transmitting antenna, and potentially overlap with Rx bands leading to interference [25, 53, 54, 55].

Based on this analysis, external sources can be viewed as antennas of PIM. Even though the sources are beyond the antenna, e.g., are external to the radio, the physics of PIM from internal sources, namely MIM junctions, are the main contributors to radiate PIM towards the Tx antenna. As any antenna, it is characterized by its parameters, how- ever, these can not be measured. , polarization, directivity, gain, are all dependent on the strength of the current induced and how it flows in the surface. Additionally, one external source can have multiple MIM junctions and reflections con- tributing to the radiation of IM products. There is also uncontrollable variables that can affect this generation such as dielectric coating and incident wave polarization. So, it is feasible to assume that, depending on the external source it is encountered by the transmitted tones, different PIM antennas ought to be expected.

2.5 Discussion

In this chapter, nonlinear behavior was shown to be a consistent problem in passive com- ponents of the radio systems. The nonlinearities are prone to cause IMD when signals containing two or more carriers frequencies flow through these sources. The spurious spectral content created due to the nonlinear I-V relation in a nonlinear device can in- terfere with the Rx bands. Heterodyning by passive devices, or PIM, is a concerning problem due to the several possible sources, for instance, connectors, cables, antennas, metallic objects, corrosion, etc. and for being unavoidable. Furthermore, two types of PIM sources were identified and discussed, internal or external, depending on where they are encountered by the Tx tones in the radio system and which mechanisms generate the nonlinear behavior. For internal sources, the main triggers of nonlinearity are MIM junctions and ET conductivity which were discussed in detail. It is concluded that MIM Fundamentals of Passive Intermodulation 22 junctions cause electron tunneling and ET effects by heat conduction and dissipation, lead to a nonlinear I-V relation that create IM products when signals interact with the component. For external sources, an overview of the generation mechanism based on the TDPO approach is presented. Nonlinear currents are induced on external metal- lic objects which cause IM products to be radiated back, especially when the current flows through nonlinear junctions (MIM) of the object. For both types of PIM sources, each mechanism is seen as individual contributors for the interfering signal, i.e., a PIM transmitter. Hence, one passive source can have multiple PIM contributors (Txs) which exacerbate the PIM signal, and each radio system can have multiple passive sources. Chapter 3

PIM Distortion in Radio Systems

The continuous desire for higher data rates, lower latencies, higher capacity, wider cover- age and system diversity lead to the unceasing development of improving radio systems. The mobile communication technologies, often divided into generations, started with the analog radio systems in 1980, referred to as 1G. Since then, it has been evolving until the present day, where 5G is on the brink of release for certain services. Notwithstanding, 2G, 3G, and 4G, will still remain as the primary commercial services offered by opera- tors in the near future. In general, modern radio systems are operating at a very high power, and support multiple bands simultaneously. This makes spectrum management tremendously important to ensure a reliable link, free of interfering signals.

Unpredictable nonlinearities of passive components that generate new frequency con- tents, i.e., PIM interference, presents itself as a major source of interference. The gen- esis of spurious signals that can potentially block a receiving channel or can severely reduce the channel to interference ratio, as was explained in 2.2. This type of distortion is accounted in specifications for different types of mobile networks. For instance, in a narrowband (NB) network like GSM, intermodulation products level within Rx bands should not exceed -103 dBm [56]. However, it is in wideband (WB) networks such as 4G and 5G, where PIM interference turns into a more serious issue. Chances of cross channel and co-channel interference are increased due to the widening of the bandwidth. This concept is further explained later in this chapter, in section 3.2. First, we address the evolution of radio networks in this chapter. Then, we characterize the mitigation techniques that are typically adopted for PIM suppression.

23 PIM in Wireless Networks 24

3.1 Evolution of Wireless Networks

The 3GPP unites telecommunications standard development organizations together with the International Telecommunication Union, Radio Communication Sector (ITU-R) to define standards and spectrum efficiency in telecommunication radio access network (RAN) technologies through technical reports and specifications [3, 57]. In this section, we present a brief overview on the advances in mobile radio communications systems, namely, GSM, LTE, LTE-Advanced and NR. The principles supporting these systems such as transmission schemes, physical layer processing and spectrum allocation are described.

3.1.1 Overview of 3GPP Global System for Mobile Communications

GSM was the first digital radio service deployed, i.e., the first to specify digital modu- lation and network level architectures and services. It is a narrowband system, where channel bandwidth is 200kHz, and is based on TDMA and FDD. Furthermore, it was the first mobile network that allowed hardware to function on different countries. Even though there are better radio systems have since been developed and deployed, GSM hardware is still incorporated into millions of devices and will remain as the most com- mon cellular standard until 2025.

This radio system utilizes two bands of 25 MHz, 890-915 MHz and 935-960 MHz, for uplink and downlink, respectively. The Rx band is divided into 128 channels each with 200 kHz, and can be shared by eight users. Taking out 200 kHz as a guard band at the lower end of each band will leave 124 paired duplex channels with 45 MHz spacing. Each of the 124 channels operates at different carrier frequency. Most of transmission time of the slot is reserved for two bursts of 58 bits each. A combination of a time slot number and a carrier frequency number form a physical channel number that will be assigned to a user during the call [58, 59].

GSM services are divided into telephone services and data services. To operate, the system is divided into three subsystems, Network and Switching Subsystem (NNS), Base Station Subsystem (BSS) and Operation Support Subsystem (OSS). However it is the BSS that is associated with channel management, transmission functions, and radio link control [58, 59]. Interference issues are then captured by BSS and expected to be handled by the OSS.

This technology was then enhanced by implementing a packet-switch domain in addition to the circuit-switch domain- General Packet Radio Service (GPRS) is one of the packet- data protocols embedded to the GSM. The combination of both technologies is often refereed to as 2.5G and provides data rates of 100 kbps. It was also the beginning of the PIM in Wireless Networks 25 development of the 3G technology since it shares some of the radio network elements. UMTS has increased data rates and enlarged carrier bandwidth. However, we will not draft an overview of this wideband technology since, for the context of this thesis, the PIM interference problem can be studied in the broadband LTE radio.

3.1.2 Overview of 3GPP Long Term Evolution

LTE evolved by focusing on packet-switch data domain, revolutionizing radio-access technology. The drivers behind this evolution were the new set of performance and ca- pability targets defined by the 3GPP in the first phase of the project. These requirements are derived to enhance peak data rates, user system throughput, spectral efficiency, la- tency and other specifications such as spectrum flexibility and interaction with other existing technologies (GSM, UMTS). These parameters were essential drivers in the de- sign of LTE network and were achieved throughout three 3GPP releases, Release 8 - Release 10.

These releases contain the basic functionalities of LTE, protocol, physical layer, chan- nels, data flow, etc. In case of the LTE downlink, the transmission scheme is based on conventional OFDM which provides a high degree of robustness against channel fre- quency selectivity as well as access to the frequency domain and a flexible broadcast transmission bandwidth. The LTE uplink is also based on OFDM transmission how- ever, in data transmission, the OFDM modulator is preceded by a Discrete Fourier transform (DFT) precoder. This leads to a DFT-spread OFDM (DFTS-OFDM), also known as SC-FDMA, to reduce the cubic metric (CM) of the uplink transmission. This enables higher terminal power-amplifier efficiency and orthogonal separation of uplink transmissions in the frequency domain. [60]

In addition to the radio access schemes employed, LTE also offers a high degree of spectrum flexibility. The goal of this flexibility is to allow the deployment of LTE radio access in several frequency bands with diverse characteristics, including different duplex arrangements and different sizes of the available spectrum. In other words, LTE supports both TDD and FDD on both downlink and uplink transmissions, respectively. Consequently, LTE manages to support data rates according to the available spectrum (wider the band the higher the rate) peaking at 100 Mbps in the downlink and 50 Mbps in the uplink. In addition to the RF flexibility, MIMO technology was also introduced in this technology. The main principles of the physical layer are explained in the following subsection. PIM in Wireless Networks 26

3.1.2.1 OFDMA and SC-FDMA Principles

LTE downlink radio access is achieved via OFDMA, a multicarrier transmission and multiple access scheme. In this scheme, the available transmission bandwidth is split into several narrow bandwidth orthogonal subcarriers, with each subcarrier carrying data. Different users can be flexibly mapped to different subsets of the overall pool of subcarriers. OFDM is used as a multiple access scheme that allows for simultaneous frequency separated transmissions from multiple terminals [16, 60]. The advantages of using OFDMA derives from the orthogonality between subcarriers, achieved through careful selection of the carrier spacing, i.e., at the center of a subcarrier, zero crossings are made by the remaining. In LTE, the basic subcarrier spacing is 15kHz and the number of subcarriers varies according to the occupied bandwidth. Users can be allocated to any of the subcarriers in the frequency domain, however, the allocation is based on resource blocks (RB). A resource block consists of a group of 12 adjacent subcarriers, which corresponds to a bandwidth of 180 kHz. In the time domain, LTE transmissions are organized into frames of length 10 ms, each divided in ten equally sized subframes of 1ms and each subframe consists of two equally sized slots of length 0.5ms. Theses slots carry a number of OFDM symbols including cyclic prefix (CP), which usually amounts to seven data symbols. In sum, LTE downlink transmission supports two frame structures: frame structure type 1, applicable to FDD and frame structure type 2, applicable to TDD. In Figure 3.1, both types of frame are represented.

A drawback of the multicarrier OFDMA transmission scheme is that the simultaneous transmission of subcarriers leads to large variations of instantaneous power, i.e., high peak-to-average power ratio (PAPR). So, due to power limitations of user equipments, the uplink transmission scheme is based on a different OFDMA access method, DFT- spread OFDMA or SC-FDMA [16, 60, 61]. SC-FDMA can be viewed as OFDM with a DFT-based precoding, whose main benefit are the reduced variations in the instanta- neous transmission power (lower PAPR). This is due to the DFT operation performed on modulated data symbols which spreads the data over all the subcarriers instead of the usual symbol per subcarrier ratio used in OFDM. The uplink radio frames are similar to the downlink transmission displayed in Figure 3.1.

3.1.3 Overview of 3GPP Long Term Evolution-Advanced

Even though tremendous achievements were already achieved with LTE, the ever in- creasing demands of higher data rates for mobile users caused the ITU-Radio (ITU-R) to define a new set of requirements called IMT-Advanced [62]. These were the target goals of the following 3GPP release, Release 10. Henceforth, the name LTE-Advanced refers to any technology added after this release, but mainly referencing 3GPP Release PIM in Wireless Networks 27

1 Frame (10 msec)

1 Sub-Frame (1 msec) 1 Slot (0.5 msec)

1 2 3 4 ...... 10 ...... 18 19

01 2 3 4 5 6

Cyclic Prefixes

7 OFDM Symbols (short cyclic prefix) LTE Frame Type 1 (a)

1 Frame (10 msec)

1 Half-Frame (5 msec)

Subframe 0 Subframe 1 Subframe 4 Subframe 9

DL Pilot UL Pilot DL Pilot Guard Guard UL Pilot Time Slot Time Slot Time Slot Period Period Time Slot

LTE Frame Type 2 (b)

Fig. 3.1: LTE frame structures: (a) Frame structure type 1 applicable to FDD and half duplex FDD; (b) Frame structure type 2 applicable only to TDD

10. Overall, LTE-Advanced covers 3GPP Release 10 through Release 14 and, at the time of writing of this thesis, is the most advanced radio network commercially available [16, 60]. In terms of features, LTE-Advanced incorporates a multitude of enhancements that can be grouped in three major categories: 1) Carrier aggregation (CA) that bonds multiple carriers together to provide extremely high data rates; 2) Advanced antenna techniques to improve spectral efficiency; 3) Heterogeneous Networks optimizations to bring more out of small cells. Among these main categories, we only described the CA principle in more detail as it is particularly relevant in the context of PIM interference problem.

In the previous section, some general relevant properties of LTE regarding physical layer were introduced. For LTE-Advanced, most of these properties remain similar yet, mostly due to CA, some changes in both uplink and downlink are introduced. For instance, while LTE supports scalable bandwidths with 6 different carrier bandwidths, PIM in Wireless Networks 28 i.e., 1.4, 3, 5, 10, 15 and 20 MHz, however, CA techniques introduced in LTE-Advanced enable considerably larger bandwidths and, consequently, higher data rates across the cell coverage area (over 1 Gbps in the downlink). Together with CA, multi-cluster transmission was also introduced (although it was not until 3GPP Release 11), which allows for a more flexible channel-dependent scheduling at the uplink, but at the cost of increasing PAPR. Other notable features achieved throughout the 3GPP LTE-Advanced releases include improved spectral efficiency, low latency, multi-antenna transmission, and backward compatibility with legacy LTE systems. [16, 63]

3.1.3.1 Carrier Aggregation Fundamentals

CA has a crucial role in fulfilling the data rate requirements defined by ITU-R. The peak data rate requirements are fulfilled by realizing a large transmission bandwidth, where multiple legacy LTE carriers, each with up to 20 MHz bandwidth and called com- ponent carriers (CCs), are combined. Hence, CA is an intriguing approach as it allows operators to deploy a system with extended bandwidth by aggregating several smaller component carriers (CC) while providing backward compatibility to legacy users [64, 65]. This technique also provides an increase in spectrum flexibility and efficient spectrum utilization since data traffic is asymmetric, i.e., the number of aggregated CCs of the uplink and downlink can be different [66, 67, 68]. However, the number of aggregated CCs in the uplink is always less than or equal to the number of aggregated CCs in the downlink. There are two possible scenarios of CA are possible: contiguous CA, and noncontiguous aggregation CA. The noncontiguous CA can be within one frequency band (intraband) or spread over multiple bands (interband) [64, 65, 66]. In Figure 3.2 it is represented both types of CA. The interband case allows network operators to fully utilize their spectrum resources, i.e., scattered frequency bands over the RF spectrum. In early releases of LTE-A, up to five CCs could be aggregated, amounting to 100 MHz in operation bandwidth, however, currently it can go as high as combinations allow. The complexity of noncontiguous CA is much higher compared to contiguous CA since the multi-carrier signal can not be treated as a single signal. Also, given the fact that the spectrum resources are scarce in low frequency bands (< 4 GHz), it is difficult to allocate contiguous 100 MHz of bandwidth. However, in UE, it is easier to implement contiguous CA [3, 66]. In the context of PIM interference, it is preferable to focus on noncontiguous CA since the intermodulation problem is harder to deal with in this case as it is explained further ahead in section 3.2.1. PIM in Wireless Networks 29

10 MHz20 MHz 10 MHz 20 MHz 10 MHz

Carrier 1 Carrier 2 Carrier 3 Carrier 4 Carrier 5 f [MHz] (a)

10 MHz 20 MHz 10 MHz

Carrier 1 Carrier 2 Carrier 3 f [MHz] (b)

Fig. 3.2: Types of CA: (a) Contiguous CA of several 10 and 20 MHz carriers; (b) Noncontiguous CA of carriers of 10 and 20 MHz carriers

3.1.4 Overview of 3GPP New Radio

Thus far, we have examined some of key principles in existing radio systems, however, two more 3GPP Releases can be accounted for, Release 15 and Release 16, respectively . With these releases a new generation of mobile communication is being introduced, 5G, commonly refereed to as NR. This network is capable of enormously expanding the capabilities of current networks since it is expected to provide extreme data rates, ubiq- uitous coverage, ultra-reliability, very low latency, high energy efficiency, and a massive number of heterogeneous connections. Nonetheless, there are three major challenges that 5G is required to tackle: massive growth in the number of connected devices, mas- sive growth in traffic volume and a wide range of applications with diverse requirements and characteristics. [69, 70, 71]

Similar to 4G LTE-A technology, an ITU-R recommendation defines the requirements for 5G. It is called IMT-2020, and started being developed with 3GPP Release 15 and is expected to be finished with 3GPP Release 16 [72]. Some key capabilities of IMT-2020 are, peak data rates of 20 Gbit/s, average data rates of 200 Mbit/s, latency of 1 ms, etc. These requirements induced the main change in 5G technology, previously mentioned, the use of higher frequencies in the millimeter-wave range. Supporting frequencies below 1 GHz and up to 100 GHz allows for larger bandwidths, in the range of several GHz. However, the use of millimeter waves brings up several challenges, thus 5G must be designed for flexible frequency use over the available spectrum. Spectrum flexibility and operation in both sides of the spectrum provides both reliable coverage and very high capacity. In total, 5G will provide three types of communications based on their main features: enhanced mobile broadband (eMBB), massive machine-type communications (mMTC), and ultra-reliable low-latency communications (URLLC) [69, 70, 71]. For these three network subsystems, a complex physical layer was split into different layers. The main properties of the physical layer are explained in the following subsection. PIM in Wireless Networks 30

3.1.4.1 NR Physical Layer Principles

The NR physical layer handles coding/decoding, modulation/demodulation, multiantenna processing, and mapping of signals to physical time-frequency resources. As in LTE, it supports different modulation schemes (different options of QPSK and QAM), that can be adopted based flexibly. Additionally, NR employs cyclic prefix OFDM in both uplink and downlink up to at least 52 GHz , with an option to use DFT-spread OFDM (SC- FDMA) in uplink for coverage limited scenarios. This is different compared with LTE, where CP-OFDM is only used for downlink transmission and SC-FDMA is used solely for uplink transmissions. NR also possesses a scalable OFDM numerology to enable diverse services on a wide range of frequencies and deployments. The subcarrier spacing is scalable, i.e., 15 kHz, 30 kHz, 60 kHz and 120 kHz, with normal CP included as in LTE. The number of active subcarriers in Release 15 is 3300, whose combinations with the different bandwidths, allows for maximum bandwidths of 400 MHz. Finally, carrier aggregation can also be employed, supporting up to 16 CCs [70, 71, 73].

With OFDM transmission scheme for both downlink and uplink, it is observed that NR also supports both TDD and FDD transmission. NR also supports dynamic TDD, where uplink and downlink allocations dynamically change over time [71]. In the time domain, each radio frame has a duration of 10 ms and consists of 10 subframes with a duration of 1 ms. A subframe is formed by one or multiple slots, each slot with 14 adjacent OFDM symbols. A mini-slot is restricted to either 2,4 and 7 OFDM symbols, and is used to support transmissions with a flexible start position. This feature is particularly useful for low latency transmissions and transmissions in the millimeter wave spectrum. The time duration of a slot/mini-slot scales with the chosen subcarrier spacing [70, 71, 73]. Figure 3.3 shows an example of an NR radio frame.

Finally, physical time-frequency resources correspond to OFDM symbols and subcarriers within the OFDM symbols. The smallest physical time-frequency resource consists of one subcarrier in one OFDM symbol, previously defined as a resource element. Similar to LTE, the transmissions are scheduled in group(s) of 12 subcarriers, RB. Yet, in contrast to LTE, the reference signals in NR are only transmitted when necessary, typically at the beginning of a slot [70, 71, 73]. To support the increase in channel capacity and operation in the new part of the RF spectrum, multi-user MIMO (or massive MIMO) and beamforming are introduced in NR. There is a support to increased number of antennas (over 100) and connectors in the BS. PIM in Wireless Networks 31

1 Radio Frame (10 msec)

1 Sub-Frame (1 msec)

0 1 2 3 4 5 6 7 8 9

1 2 3 ...... 12 13 14

1 Slot (1 msec) with 14 OFDM symbols (15 kHz subcarrier spacing)

1 2 3 ...... 13 14 1 ...... 12 13 14

2 Slot (0.5 msec each) with 14 OFDM symbols each(30 kHz subcarrier spacing)

1 ...... 14 1 ...... 14 1 ...... 14 1 14

4 Slot (0.25 msec each) with 14 OFDM symbols each (60 kHz subcarrier spacing)

Fig. 3.3: NR radio frame transmitted per TDD topology with the flexible subcarrier spacing derived from basic 15 kHz subcarrier spacing

3.2 Passive Intermodulation Distortion in Radio Systems

In section 2.2, PIM was defined as an interference source in radio systems that has the potential to degrade the efficiency of a cell site, thereby directly affecting the performance of a radio network. Furthermore PIM interference problem is exacerbated due to the coexistence of multiple communication systems in the same areas, and is a growing problem as the network complexity and deployments increase. Therefore, it is a problem whose impact in networks is growing. Since PIM interference is a problem concerning RF spectrum, intermodulation issues are aggravated in broadband radio systems where bandwidth is enlarged to achieve increased data rates, particularly when CA is employed. Nonetheless, active narrowband systems like GSM are also prone to PIM interference effects. [4, 74]

Passive intermodulation is often viewed as an installation problem, mostly observed in high-power cell sites, given the nonlinear generation mechanisms. Yet, this is merely a superficial consideration, as this interference problems often arise from the saturated RF spectrum. The assiduous update and growing of the network systems turns PIM into a volatile problem, whose effects on RF systems will continue to escalate. This is particularly significant in 5G with the growth of seamless integration of multiple base station technologies [74]. Based on these considerations, this section focus on explaining PIM in radio systems, in terms of PIM generation on broadband radios and its impact on the network. PIM in Wireless Networks 32

3.2.1 Passive Intermodulation in Broadband Radio Systems

Most literature describe and analyze PIM based on two unmodulated carrier signals. As it was showed in section 2.1, in this case, the resulting PIM products are also narrow carriers spurs. However, in broadband radio systems like UMTS and LTE, the signal is modulated over a wider bandwidth and can be transmitted through several bands of the RF frequency, especially with the employment of features like CA. Furthermore, the combined modulated signals can be both narrowband or broadband at the same time. Hence, consider a general noncontiguous dual-carrier CA FDD transceiver whose Tx signal is represented as

jf1 jf2 x[n] = x1e + x2e . (3.1)

This signal is composed of two CCs, denoted by x1 and x2 and respective frequencies f1 and f2 (f1 < f2). When this noncontiguous Tx signal passes through a nonlinear passive source, mixing occurs and IM components arise. This prejudicial output is expressed as

P X y[n] = x[n] |x[n]|p−1 , (3.2) p=1 p odd where P denotes the polynomial (IM product) order. For simplicity purposes, only nonlinearity orders up to P = 5 are considered. After substituting (3.1) in (3.2) and developing the several odd order terms, P = 1, 3 and 5, we obtain two types of frequency components in addition to the original Tx signals. The first type of components are classified as spurious terms and correspond to the 3rd and 5th order IM products. As explained in section 2.1, this spurious IM products appear on both sides of the Tx signals on the spectrum with the bandwidth of equation (2.4). The 3rd order products th appear at 2f1 − f2 and 2f2 − f1 whereas the 5 order products appear at 3f1 − 2f2 and th rd 3f2 − 2f1. However, for P = 5, additional spurious 5 order products appear at the 3 th order products frequency, e.g., 5 order products appear at frequencies 2f1 − f2 and rd 2f2 − f1 in addition to the 3 order ones. Thus, the spurious components appearing on − rd th 2f1 − f2, IM3 , is the sum of the 3 and 5 order products expressed as

− 2 ∗ j(2f2−f1) IM33 = x1x2e (3.3) − − 2 2 IM35 = IM33 (2|x1| + 3|x2| ). (3.4) PIM in Wireless Networks 33

B21 UL B15 UL B2 DL B21 DL

3rd 3rd

5th 5th

1710 1755 1900 19201930 1990 2110 2155 2320 2130 1940

Fig. 3.4: Spectral regrowth given the spurious and OOB emission due to IM of carriers from B2 and B21 that can lead to interference in B15 and B21

+ The spurious components appearing on 2f2 − f1, IM3 , are simply obtained from (3.3)

and (3.4) by interchanging x1 and x2 and substituting 2f2 − f1. Regarding IM products

appearing on frequencies 3f1 − 2f2 and 3f2 − 2f1, in this case, are just composed of 5th order products. Assuming an analogous notation, the spurious components on both sides of the spectrum, IM5− and IM5+, are expressed as

− 3 ∗2 j(3f1−2f2) IM5 = x1x2 e (3.5)

+ 3 ∗2 j(3f2−2f1) IM5 = x2x1 e . (3.6)

The second type of components show up at the close vicinities of the CCs. Similarly to the first type, there are 3rd and 5th order IM products, however, these components appear as a bandwidth extension of CCs, i.e., sub-bands appear on both sides of each CC. Assuming an analogous notation, the 3rd and 5th order side bands that appear on CC1 CC1 the vicinity of the first CC, IM3sub and IM5sub respectively, are expressed as

CC1 2 2 jf1 IM3sub+ = x1 × (|x1| + 2|x2| )e (3.7)

CC1 4 2 2 4 jf1 IM5sub+ = x1 × (|x1| + 6|x1| |x2| + |x2| )e . (3.8)

CC2 The components appearing at the vicinity of the second CC, IM3sub and CC2 IM5sub , can be obtained from (3.7) and (3.8) by interchanging x1 and x2 and substi- tuting f1 for f2. Both OOB emissions and spurious emissions are classified as unwanted spectral emissions, or spectral regrowth [3, 16, 75]. Spectral regrowth can be seen as spreading of the power spectrum. The unwanted power can appear in Rx bands and cause interference to the desired receiver signal. In real scenarios, current radio systems rely on multi-carrier and multi-band technologies, so spectral regrowth due to IM can affect a wide range of the spectrum, i.e., potentially interfere with several Rx bands. PIM in Wireless Networks 34

RU1 RU1 RU1

PIM

External PIM Source

Fig. 3.5: Cross-PIM scenario involving three radio units, RU1, RU2 and RU3 and an external source close to the BS

As an example, consider a FDD system where signals are transmitted from separate bands. Consider two channels transmitting from band 2 and band 21, B2 and B21 respectively. Band 2 DL ranges from 1930 MHz to 1990 MHz, and the transmitting carrier has a center frequency of 1940 MHz with 10 MHz of bandwidth. Band 21 DL ranges from 2110 MHz to 2155 MHz, and the transmitting carrier has a center frequency of 2130 MHz with 10 MHz of bandwidth. Due to a nonlinearity on a passive device during the transmission, PIM products are generated. As a result, one of the generated spurious 3rd order and fifth order IM products will overlap with the receiver band of B21, comprised between 1710 MHz and 1765 MHz, since they are centered around which 1750 MHz. In addition, OOB 5th order product overlaps with B15 UL, as the bandwidth extension of the B2 carrier is wide enough to fall within this Rx band. Both of these scenarios lead to a potential risk of interference, even though the spurious emission is more prejudicial. Figure 3.4 portrays the example described above.

In an active broadband base station, it is common to have spectral regrowth where the carriers combined at the source are from different frequency bands. If the CCs involved in PIM generation are from multiple bands like the example above, the scenario is titled as cross-band PIM. Likewise, if the carriers are from one single band, the scenario is titled in-band PIM [76, 77]. Cross-band PIM is being exacerbated by the refarming of RF spectrum, e.g., new DL bands and interband CA, and the increase in complexity of the BS. Furthermore, cross-band PIM is a concurrent scenario in modern radio systems given that the number of external sources in which the carriers can mix is increasing. This scenario is depicted in Figure 3.6. PIM in Wireless Networks 35

3.2.2 Passive Intermodulation Impact on Network Performance and Physical Layer

The RF spectrum is divided in several bands for different services and operators. Shar- ing passive infrastructures (co-sites) has become a common strategy adopted by telecom operators due to key factors such as cost reduction, environmental impact, increased revenue, etc. [78]. It was previously established that PIM sources are mainly present in co-sites environments. Therefore, it is denoted that IM interference caused by the nonlinearities of passive components may impact the radio system performance, partic- ularly when taking into account frequency relationship between the configured bands. [4, 7, 74, 79]

In typical co-sites scenarios, standard PIM interference specifications are designed to meet -150 dBc noise floor level. In state-of-the-art radio infrastructure components, even low-level PIM may severely degrade system performance. For instance, if a com- ponent’s PIM characteristics degrade due to uncleanliness then the noise level rises to -145 dBc, which corresponds to 3 dB power loss in the uplink. In general, a reduction of 1 dB in uplink sensitivity due to PIM interference corresponds to 11% decrease in the coverage [74, 80]. This indeed translates to severe system degradation and the loss of income to the operators. In radio networks, PIM’s impact on the uplink transmission can be categorized in the cell coverage reduction, reduced system capacity and inter- cell interference. In 4G radio network where CA framework is introduced, nonlinear IM products due to PIM fall within Rx bands spread throughout the spectrum. The overall effect is an increase in noise floor and reduced margin in receivers sensitivity [80]. The PIM problem becomes further complicated in 5G networks where nonlinear inter- band intermodulation have already been identified as the main threat to the network’s performance should the principles drafted in section 3.1.4 remain, [81].

Moreover, PIM has also become a threat in high power multicarrier transmitting systems like OFDM [82]. The degradation in the performance in communication systems (in- crease in noise levels) can be quantified by (BER), symbol error rate (SER) and synchronization probabilities. The PIM effects on the BER of M-PSK and on digital channels were investigated in [83] and [84] respectively. The results show that PIM negatively affects the channel since it increases the error probability in mak- ing a decision in the detection part, however, PIM interference decreases with increasing PIM order. In the case of frame synchronization, the PIM effect was studied in [85]. The statistical properties of a time metric function (window that slides in the time domain to search for the first training symbol) in presence of PIM are the basis for analyzing the false or missing probability of the OFDM system. The results show that, in case the PIM interference makes the window function locate the symbol behind the actual start PIM in Wireless Networks 36 position, i.e., the starting position does not fall into CP, (ISI) is introduced, worsening the probabilities of both missing and false detection. In summary, it can be concluded that PIM has a severe impact on radio systems performance. In the following sections, we review commonly adopted PIM mitigation techniques.

3.3 Passive Intermodulation Mitigation Techniques

In general, PIM generated spurious signals interfering in the Rx bands are unpredictable. As previously explained, the spurious signals are dependent on the site’s environment, RF infrastructure conditions, external and internal sources respectively, as well as con- figured bands and used frequency channel. The strength of interfering signals typically depends on the nonlinear properties of the PIM causing source. Furthermore, there is also the uncontrollable aspect of dielectric coating in external sources discussed in sec- tion 2.4.2. With this, countering any PIM interference becomes a complex problem. The complexity of PIM mitigation further increases when assuming continuous enhancement of radio systems, e.g., higher performing services, smaller cells and radio configuration in the RF path. Nevertheless, until now, PIM interference has been managed with different mitigation techniques which are now briefly reviewed below.

PIM mitigation techniques can broadly be split into two categories, physical techniques and radio integrated techniques. Physical mitigation techniques are procedures or mod- ifications that can be applied to the RF equipment, infrastructure and surrounding environment to rectify or reduce the level of PIM interference. Often, these processes are specific counter measures to the generation mechanisms explained before, and imply a complete understanding of the physics associated. Digital mitigation techniques are engineered into the signal’s path and make use of processing techniques to reduce the PIM interference.

3.3.1 Physical Mitigation of Passive Intermodulation Interference

This section summarizes the guidelines followed by RF manufacturers to mitigate PIM when setting up a radio system on a site with PIM issues. For these physical endeavors, the physics of the mechanisms behind PIM described in Chapter 2 are taken into account. Since PIM sources can be either internal or external, it is logical to divide this section into two subsections to account for the physical actions to mitigate both types of sources. PIM in Wireless Networks 37

3.3.1.1 Guidelines for Mitigation of Internal Sources

To mitigate internal sources of PIM in radio systems, it is needed to counteract the effects shown in section 2.3. The following guidelines are usually adopted by manufacturers for the last couple of decades:

• Avoid the use of nonlinear components within or near the infrastructure;

• Keep current densities low in the conduction paths by using larger conductors or having bigger contact areas, e.g., MM contact;

• Minimize metallic contacts and connectors, ensuring that loose contacts and ro- tating joints are avoided;

• Keep thermal variations to the minimum in the components of the radio system;

• Have all joints clean and tight, preferably made or coated with materials less bounded to oxidation;

• Shorten the use of cables to the maximum and use semi-rigid coaxial cables;

• Achieve good isolation between the high power transmit signals and the low level receive signals (duplexer isolation);

Although no system is completely free from PIM, careful planning, good workmanship and a high standard of system maintenance are equally important to substantially reduce its level [4, 5, 17, 27, 29, 80, 86, 87, 88].

These guidelines have been applied to mitigate PIM in radio systems, however, since electro-thermal effects have been identified as the main internal PIM sources (see e.g. Section 2.3.2) low electronic conducting materials are now being employed in the man- ufacturing of radio system components. This pratice ensure that the thermal variations are kept to a minimum while employing high power currents flowing through the RF components of the base station [89].

3.3.1.2 Guidelines for Mitigation of External Sources

To mitigate external sources of PIM in radio systems, it is required to counteract the effects shown in section 2.4. However, unlike internal sources, these are more difficult to deal with as previously explained. A simple and recurrent guideline used by manu- facturers when setting up a site is scanning the environment, or RF path, for potential nonlinear sources that can generate PIM and then removing them. These scanners, for instance the PIM Hunter by Anritsu, test for primary test tones that generate IM PIM in Wireless Networks 38 products to locate the source [90]. Yet, objects on the antenna’s radiation path are unpredictable and uncontrollable which makes their mitigation a complex problem. The power of the distortion caused by these sources is also dependent on how far the source is located so, in some cases, may even be the principal PIM source. Since PIM is intrinsic to every radio system, most manufacturers turn to digital techniques to mitigate the inherent PIM. However, with the continuous increase in radio systems, section 3.1, the complexity of the base stations is also increasing, especially the number of antennas. As it was mentioned previously, MIMO systems are already implemented and will soon be upgraded to massive MIMO, with antennas playing a major role in PIM. Since their sensitivity level is getting lower, every enhancement that increases the power of the transmission link (dB) matters. It is based on these considerations that the study of Chapter 4 is performed, with the objective of lowering the complexity of PIM mitigation algorithms. The study also contributes to existing mitigation techniques of antenna isolation that will be proceeded to explain.

Antenna isolation are considerations taking in co-site base stations to avoid the excessive interference (PIM) and improve the link quality. The amount of isolation achieved is dependent on several factors such as physical horizontal and vertical separation distance between antennas, antenna polarization, radiation pattern, and surrounding environ- ment of the antenna [91, 92]. In general, the mitigation of IM interference improves with increasing separation between the antennas as well as with increasing electrical down tilt (azimuth) angle.

3.3.2 Radio Integrated Mitigation of Passive Intermodulation Inter- ference

In general, the PIM interference problem cannot be fully contained through physical PIM mitigation approaches. Therefore, recently, digital PIM mitigation approaches have started to receive an interest, see for examples [4, 91, 93, 94] among others.

The digital PIM cancellation approach is normally based on the block diagram shown in Figure 3.6. This model is based on adaptive filter theory and, the general idea is to predict PIM-induced IM products based on the transmitting signal to subtract them from the receiving signal chain (after I/Q conversion and duplexer). However, the main problem in digital cancellation is that PIM products amplitudes, phases and delays depend on the used RF components (PA, duplexer, etc.),e.g., they are not constant. This adds extra complexity in the model used for estimating the IM products since the parameters have to be adjusted or analyzed when the transreceiver system is offline. However, the main benefit of this digital cancellation is that it can be used to reduce the IM products which are generated internally, after the Tx filter. PIM in Wireless Networks 39

Fig. 3.6: Diagram block for an adaptive cancellation PIM algorithm

Another commonly employed strategy is known as frequency or resource planning. Al- though this study ([91]) was made in deployments of 2G and 3G networks, the same principles analogously apply to include 4G and 5G networks in the base stations. In this process, the distribution of available channels is chosen for every tier following a channel spacing rule. The choice of the channel allocation is made frantically so as to achieve minimization of the spurious interference signals. When superimposing the net- works, this process can be done either by block assignment or frequency banning. The first assigns blocks of channels to both networks that guarantee that no potentially IM product affects the transmission inside the cell. The second comprises of three steps: identify the channel combinations that give harmful IM products in every cell; avoid- ing the most popular channels in the combinations; compensate of the loss in capacity (number of channels) by using frequency hopping. Unlike other approaches, frequency planning completely avoids the PIM problem thereby guaranteeing a PIM-free channel. However, this approach hinders full exploitation of available resources and can lead to reduced throughput.

Some uncommon strategies can also be employed but come at a greater cost. For in- stance, reducing the transmit power can reduce PIM, as PIM power is directly related to Tx power. But this comes at a cost of reduced coverage. Another example is to improve Rx sensitivity when PIM is eminent. But this also impacts users on cell-edge which will be communicating with BS at a low power and their signals may be blocked.

3.4 Discussion

In this chapter, we firstly presented an overview of the evolution of the radio systems. We reviewed that the development of new features and techniques integrated in cur- rent radio systems like CA contribute to exacerbate the PIM interference problem. In particular the enlargement of the bandwidth in broadband radio systems and shared PIM in Wireless Networks 40 co-sites base stations where PIM is ought to be more likely due to the several frequency carriers, the spectral regrowth turns into a more serious issue. As we have showed, the mixing of these carries lead to broadband IM products that, in a highly saturated RF spectrum, are prone to overlap with Rx bands. This interference has a prejudicial effect on the network’s performance and in the detection system of the physical layer. Finally, we discuss different types of PIM mitigation techniques used by manufacturers and operators, i.e., physical and radio integrated techniques. Concerning physical miti- gation techniques, due to the extensive research on the physical generation mechanisms, several countermeasures are already employed. However, it is also due to this extensive research that we confirm that PIM is an assiduous and uncontrollable problem. Thus, radio integrated mitigation techniques are very important to assist in dealing with the unpredictability. So far, the strategy for this type of techniques was centered around predicting the spurious frequency emissions, however, with the saturation of the spec- trum, new strategies are asked for. In recent years, digital cancellation algorithms have surfaced as a viable alternative but, improvements are required for better performance. Enhancements are obtained through data collection and analysis. Chapter 4

Measurements-based Analysis of External Passive Intermodulation

Thus far, throughout this work, a characterization on PIM generation in radio sys- tems has been drafted. Building on the discussions in the previous chapters, we now hone external PIM, namely the PIM power induced in different antenna elements. For this purpose, in this chapter, we emulate and analyze different transmission scenarios with different external sources to induce PIM. In addition, several measurements were recorded for the several case studies established. Even though the main intention is to investigate and characterize the relation between external generated PIM, Tx and Rx characteristics, it is also investigated the fundamental triggers of external PIM covered in section 2.4.

Firstly, we present the measurement setup, describing the radio hardware and different PIM sources that are employed in the measurements. The external PIM sources mimic a real-world scenario of an object that can be within the RF signal path. Then, we analyze the PSD of the most likely case and measurement to introduce performance metrics for PIM measurements. Afterwards, we analyze the different measures obtained for different sources as well as the PIM changes over time. Finally, we apply a digital PIM cancellation algorithm developed by Ericsson to see how it works.

4.1 Radio Setup and Use Cases

The radio setup used in the experiments emulates the scenario described in Figure 4.1. The base station radio consists of a dual-band (B2 and B66) LTE radio connected to two cross polarized antennas, horizontally separated 90 cm. This implies that there are, in total, four antenna elements, two with +45◦ polarization and two with −45◦

41 Measurements and Analysis 42

Fig. 4.1: Measurement setup with an external PIM source, Rusty Metal Clamp polarization, each capable of transmitting and receiving the signals, i.e., serve as Tx and Rx. Linear cross polarization is generally widely adopted in radio systems, especially in broadband antenna arrays, since it lowers mutual interference [92, 95]. The antenna infrastructure is assembled inside an anechoic chamber and is connected the to the ports of the radio outside the chamber through coaxial cables and . For evaluation purposes, we transmit and receive only on Band2, whose downlink band is comprised of interval 1930 - 1990 MHz while the uplink band is comprised of interval 1850 - 1910 MHz. The duplex gap, in general, is 80 MHz, however, it can drastically reduce down to only 20 MHz if the carriers are configured for transmission at the edges of the band. This experimental setup ensures that 3rd order cross-modulation products of the DL carriers center frequencies can fall within the Rx band, and we may observe PIM interference in the uplink band.

In the transmission, we adopt a multicarrier Tx signal (dual-carrier DL signals), which is modulated with a 64-QAM modulation scheme and carriers with bandwidth of 5 MHz. The DL carriers center frequency are 1930 MHz and 1985 MHz which makes the prejudicial 3rd order PIM product centered around 1875 MHz. In addition, the data transmitted on each antenna element is uncorrelated. Despite only being observed the 3rd order product, several higher order PIM products can also be present due to broadband TX carriers. Consequentially, when mentioning PIM distortion power level in each measurement, it refers to the power ratio of the 3rd order PIM product signal relative to the carrier, generated by the external source. The Tx power used to transmit the DL carriers is 5 W in each antenna element, and the induced external PIM is observed in the Rx chain. In the antenna’s beam we placed three different types of objects prompted to generate external PIM given the mechanisms explained in Chapter Measurements and Analysis 43

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Fig. 4.2: External PIM sources used for the measurements: (a) Steel Wool; (b) Clean Metal Clamp attached to small support structure (MCS); (c) Rusty Metal Clamp at- tached to small support structure (Rusty MCS)

2 namely, steel wool; clean metal clamp attached to small support structure; rusty metal clamp attached to small support structure. Since the goal of the research is to investigate external PIM, the guidelines of section 3.3.1 were followed to minimize internal mechanisms of PIM generation. Additionally, external PIM from scattering on the absorbent material inside the chamber can also contribute towards the PIM power level. However, the PIM power level without any external source was measured (calibration), and the value obtained was -160 dB so this contribution can be disregarded. Figure 4.1 presents the setup inside the anechoic chamber.

Given the radio setup described, nine measurements are drafted for each source. In every measurement, the PIM distortion is measured on each antenna element, i.e., all four antenna elements function as receivers (4R). The variation between the measurements is the number of active transmitters, which can be either one, two, or four, referred to as 1T, 2T, and 4T, respectively. In 1T cases, the transmitter is linearly polarized at +45◦ or −45◦ in one of the antennas (A1 or A2), which amounts to a total of four distinct combinations. In 2T cases, the transmitters are linearly polarized at +45◦ or −45◦ in both antennas (A1 and A2), which amounts to a total of four combinations as well. And, in the 4T case, the transmitters are all four branches linearly polarized at +45◦ and −45◦ in both antennas (A1 and A2). Measurements and Analysis 44

The first source tested for this research is a piece of steel wool, which was molded into a block. This emulates the transmission into a rough metal surface, derived from a physical deformation, or a curled metal fence or wire. The second source tested in this research was a metal clamp attached to a small support structure. The metal was cleaned and free of dirt particles to review different generation mechanisms. This emulates the presence of metallic objects in the RF path. The third and final source tested in this research was a rusty metal clamp attached to a small antenna structure, similar to second source but oxidized. This emulates the presence of rusty metal objects in the transmission path. For the nine cases referenced above, every source was placed at a distance d = 1.32m, and the PIM distortion observed on each branch for each case was measured. Note that, whilst comparing both of the metal clamp sources, the image of the rusty source has additional screws. However, equal ones were incorporated in the clean source despite not being displayed. In the following sections, the results from these measurements are displayed and analyzed. Figure 4.2 presents each source just described.

4.2 Power Spectral Density Analysis

The measure that better approximates a real case in radio system is the 4T4R case. We plotted the observed PIM relative to the noise floor. For each antenna element it is plotted the PSD of the PIM distortion. Additionally, every case was measured at least twice to support the validity of the results obtained. In every measure, the PSDs showed that external PIM exits, generated by the external sources, and it affects all of the branches (receivers). So, in this transmission, external PIM characterizes the interference problem in the BS.

In Figure 4.3, it is presented the 4T4R measurements for each source. In each plot, each line represents the PIM power level in each of the antenna elements. For instance, the red line and the black line represent the branches linearly polarized −45◦ and +45◦ in A1 respectively, whereas the blue and the pink line represent the branches linearly polarized −45◦ and +45◦ in A2 respectively. Figure 4.3a plots the PIM distortion with steel wool as a PIM source, Figure 4.3b plots the distortion with a clean metal clamp as a PIM source, and Figure 4.3c plots the distortion with a rusty metal clamp as a PIM source. Based on these plots, it can be confirmed that PIM distortion occurs and is a problem in the BS as it is received by both antennas. Note as every plot is normalized, hence the PIM power level can be measured in dBs.

In Figure 4.3a, steel wool case, the PIM power is higher in A2, peaking at 30 dB above the noise floor for the branch linearly polarized +45◦. In A1, the PIM power is a couple dB’s lower but its still stronger on the branch linearly polarized +45◦. In Figure 4.3b, Measurements and Analysis 45

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Fig. 4.3: PSD curves of the measured PIM on different antenna elements and with different PIM source in 4T4R configuration: (a) Steel wool as PIM source; (b) Clean metal clamp as PIM source; (c) Rusty metal clamp as PIM source. clean metal clamp attached to antenna structure, PIM power is stronger on the branches linearly polarized −45◦ with 22 dB and 19 dB for A1 and A2 respectively. Between the branches linearly polarized +45◦, PIM is stronger in A2. In Figure 4.3c, rusty metal clamp attached to antenna structure, the PIM power is stronger in A1, especially in the branch linearly polarized +45◦ peaking at 35 dB above the noise floor. In addition, in A2, PIM is stronger in the branch linearly polarized +45◦. Comparing the three plots, it can be concluded that there is not a dominant type of polarization where the PIM power is better or worse. For instance, in the clean metal case, the order from highest to lowest PIM distortion on each antenna element is −45◦ A2, −45◦ A1, +45◦ A2, and +45◦ A1, whereas in the rusty metal case the order is +45◦ A1, −45◦ A1, +45◦ A2, and −45◦ A2. Additionally, comparing the observed PIM power in each antenna element, of the clean metal and the rusty metal, it is higher in the rusty metal clamp, except for the branch linearly polarized −45◦ in A2. Note as the only difference between both sources is oxidization and exposition (more directive towards the antennas) of the rusty Measurements and Analysis 46 source. These small changes are enough to affect the strength of the interfering signal (PIM) and to cause an inconsistency in the strength of received PIM distortion in the same receivers. In the following section this analysis is applied for every measure of each source and the derived conclusion from the study.

4.3 External PIM Analysis for Case Studies

As it was mentioned in Section 4.1, measurements were made for all the 27 cases. For each case, a PSD analysis similar to the one described in the previous section is per- formed. Based on this analysis, a characterization of PIM power from the Tx side is drafted on Table 4.1. This table contains the total PIM power observed, e.g., sum of the power received in different antenna elements. Like it was mentioned in the previous section, the PIM distortion values vary in every branch, for different measurements, hence the discrepancy of the values. This is mainly due to the inconsistency of the generation mechanisms explained in Chapter 2. For instance, according to section 2.4.1 and 2.4.2, the PIM product generated of the illuminated part (area where radio beam incides) of the source is one of the contributors of the interference. This means that the PIM products generated and reflected are highly directional. However, depending on the topography of the dielectric coating, both the strength and the scattering of the IM products are affected. The loss in signal strength and divergence of received values in each branch is also due to a change in wave polarization, from a linearly polarized one to a random one, and to the change of the source’s reflection coefficient. This random wave polarization reflected back is differently coupled by the antenna elements, which explains the variances in the observed PIM. The reflection coefficient affects how much of the incident wave is scattered of the medium (in this case the coated source), which also affects the strength of the PIM product. The main contributor for external PIM is the gap between metals that behave like contact mechanisms, e.g., the “Rusty Bolt” effect. As explained in Section 2.4.3, when the incident waves lits part of the external source, a nonlinear current is formed. This current travels through the surface of the source and it can encounter small air gaps or thin electric layers between metal extrem- ities which generate PIM products. These products generated of MIM junctions are emitted towards the antennas with a random polarization. With an oxidation layer, other MIM cases can appear beyond gaps in the source, which contribute for the total PIM observed. Based on this considerations, we can assess that each external source has its own number of PIM generators, inherent to the source topology. Measurements and Analysis 47

Table 4.1: Total PIM power observed for the several configurations (dB)

Total PIM Power (dB) Case Study Tx Ant. Element Steel Wool MCS Rusty MCS +45◦ A1 31 35 24 −45◦ A1 35 20 32 1T4R +45◦ A2 33 39 22 −45◦ A2 37 36 47 +45◦ A1/A2 27 38 24 −45◦ A1/A2 35 24 38 2T4R +45◦/−45◦, A1/A2 34 37 30 −45◦/+45◦, A1/A2 32 31 25 4T4R ±45◦, A1/A2 35 25 34

In every measure, we always ensure that the total Tx power remains the same as we add more DL carriers. However, adding more DL carriers whose signals have different polarizations does not increase the PIM distortion. For example, with the steel wool source, the highest PIM distortion power is received is the 1T4R transmission (37 dB) whereas in 2T and 4T4R cases it is less or equal. The same can be observed if it is looked at the values for the two other sources. As explained in the previous paragraph, a possibility to explain this is that, with the extra amount of carriers, a destructive interference when generating PIM is being created in the source, or the polarization of the extra signals being reflected or created by the MIM junctions is more randomized. The inconsistency of the values from the aforementioned table and from the PSDs confirm the inability to detect a specific pattern common to different kinds of sources. For instance, the antenna element with the worse level of PIM is not the same for the different sources even though the configuration is the same. The antenna element with the worst level of PIM also varies when changing the configuration for the same source. So, external PIM is an interference that is also derived from the conditions the source is exposed to when interfering with the transmission. For different sources, different powers of received PIM signals ought to be expected, as highlighted in Table 4.2. Measurements and Analysis 48

Table 4.2: Variation on PIM power level for different sources relative to Tx polariza- tion

Observed PIM power and Ant. Polarization PIM Source Min Max Steel Wool 27/ +45◦ 37/ −45◦ MCS 20/ −45◦ 39/ +45◦ Rusty MCS 22/ +45◦ 47/ −45◦

In Table 4.2, it is also indicated which polarization does the limit correspond to. Looking at the polarization values it appears the polarization for the branch with the maximum PIM value is opposite to the one with the lowest. Furthermore, from both tables, its derived that oxidization, i.e., creation of a dielectric layer, worsens the problem (as expected).

For the different test cases, several measurements are made to assess the consistency of the PIM values when measured in different time instants. This helps to characterize PIM from the Rx side. For comparison reasons, in Figure 4.4, it is presented the 4T4R cases of the metal clamp sources (clean and rusty) measured in different instants. Figure 4.4a, plots the total PIM power Rx in each measure for both the clean and the rusty case. Even though there are some deviations, for the clean source case, it is observed an average of 25 dB of PIM distortion in the Rx, whereas, for the rusty source case, the Rx receives an average of 34 dB. Figures 4.4b and 4.4c, plot the PIM power received per antenna element in different measurements. For different measurements, the PIM power values appear to vary similar for the same polarization, i.e., for different measurements, the branches with equal polarization, +45◦ and −45◦, show the same amount of increase or decrease despite belonging to different antennas. Although the values in each iteration may oscillate, the interval between same polarizations is maintained. Hence, the consistency of a certain polarization being worst in one antenna is a useful result as it can lead to improvements in real time optimization. In addition, we also observe that the PIM distortion values observed in the Rx vary tremendously, especially in the rusty source case. In the rusty source case, we observe that the PIM distortion values can vary, at most, 15 dB between different measurements at each antenna element. In the clean source case, we observe that the PIM distortion values vary, at most, 7 dB between different measurements at each antenna element. However this variance can be attributed to the adoption of multicarrier signal with high PAPR values.

Since the measurements are simulated inside an anechoic chamber, to assess the validity of the analysis from the previous paragraph, we repeat the measurements for the rusty metal clamp source. Thus, Figure 4.5 shows the total observed PIM distortion values Measurements and Analysis 49

45 40 Clean Metal Clamp PIM in Band2 UL-A (-45deg,RU-1) PIM in Band2 UL-B(-45deg,RU-2) 40 Rusty Metal Clamp 35 PIM in Band2 UL-C(+45deg,RU-2) PIM in Band2 UL-D(+45deg,RU-1) 35 30

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Fig. 4.4: Total observed PIM distortion relative to the noise floor in different instants for 4T4R configuration: (a) Steel wool as PIM source; (b) Clean metal clamp as PIM source; (c) Rusty metal clamp as PIM source. relative to the noise for different configurations in several measurements. Comparing the 4T4R plot of Figure 4.5 to the plot of Figure 4.4a we can see that the observed PIM power has lowered around 10 dB even though the setup is identical. For the 2T4R case displayed in Figure 4.5, we observe that the total PIM power does not vary besides a couple of dB. However, for the 1T4R case, the total PIM power observed displays some variance, to a max of 7 dB. Lastly, again with the 4T4R configuration, we reproduced the measurements with the rusty metal clamp rotated −45◦ clockwise to see whether it has an effect in the level of PIM distortion. As it can be seen in Figure 4.5, the total PIM power observed is lower after the source was rotated. To better interpret the results, the average of the observed PIM values through the repeated measurements in each antenna elements are shown in Table 4.3. From this table and the aforementioned figure it is derived that the external source, e.g., the rusty metal clamp, generates a PIM signal that has a spatial distribution of gain. Furthermore, we also confirmed that changing small conditions in the measurements, for instance, rotating the source, changing its height Measurements and Analysis 50

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Observed PIM power relative to the noise floor (dB) Antenna Element Rusty Metal Clamp Rusty Metal Clamp rotated −45◦ −45◦ A1 17.8 17.5 −45◦ A2 12.23 17.47 +45◦ A2 8.88 8.19 +45◦ A1 17.95 9.9

Table 4.3: Comparing observed PIM power values on antenna elements after rotating the external source, Rusty Metal Clamp relative to the floor, or simply touching the rust of the source affects the current’s path and consequentially, the polarization of the PIMP products emitted.

In summary, we assess the stability of PIM induced by external sources. Despite main- taining the measurement setup throughout the testing of the several configurations, the PIM distortion observed can be very unstable and the values can differ in different days of experimentation. This variation can be attributed to changing in the conditions of the setup (only being visually identical) or stress built on by the radio throughout the measurements. However, we have confirmed that an external PIM source can be viewed as a reflective PIM antenna, where nonlinear currents produced on the surface generate the PIMP products. Hence, each source or antenna has its own broad spectrum of direc- tivity and gain, that is dependent on its conditions and format. In turn, the conditions that the source is exposed to can affect the PIM distortion captured by the Rx of radio system. In the following section, we apply digital PIM mitigation algorithm developed by Ericsson to one of the measurements to review its performance in mitigating the interference. Measurements and Analysis 51

4.4 Digital Cancellation of PIM

In Section 3.3.2, digital cancellation of PIM was highlighted as one potential PIM mitiga- tion approach. In fact, since the saturation of the RF spectrum makes PIM interference unavoidable, this mitigation technique has become the main research focus of radio inte- grated mitigation techniques. As it was explained, the idea of PIM’s digital cancellation is to create an opposite-phase digital replica of true RF PIM interference in the digital domain, and then add it to the baseband received signal. In general, PIM can be viewed as a nonlinear filtering on the transmitted signals, which are already known inside the radio. Therefore, one can exploit the deterministic nature of PIM for building a digital model and its cancellation.

In a most recent application, [94], the author employed an adaptive filter for the interfer- ence cancellation. In this technique, the filter (linear combiner) cancels the interference by adaptively adjusting its coefficients such as the output signal is as close as possi- ble to the desired signal. To generate the parameters, it is used two popular adaptive algorithms, LMS and RLS (the better choice depends on how much computational com- plexity is available). Combining these into a cancellation block alongside some other digital signal processes, it is feasible to correctly estimate coefficients, compensate for phase distortion and track PIM in real time. In the scenario when PIM distortion is present, it was possible to suppress third-order PIM.

The purpose of this section is to see if we can cancel PIM observed on the clean and rusty MCS sources, while employing a similar cancellation algorithm. The digital cancellation is for the case of 4T4R, i.e., there are 4 unique downlink Tx data while PIM cancellation is only pursued on only one uplink branch. The digital cancellation is based on Least Squares (LS) model fitting principle, and only third-order PIM is modeled and canceled. Figure 4.6 displays the received signal’s PSD after the algorithm was applied.

By analyzing the Figures 4.6a and 4.6b, we can deduce that PIM of clean and rusty MCS can be suppressed to a certain extent with digital PIM cancellation. The cancellation is in the order of 15 dB, with only third-order PIM modeling. The residual PIM is due to higher-order of PIM, that can potentially be mitigated by modeling them. However, here the intention is to only demonstrate the digital cancellation capability, and showing that digital cancellation is indeed an intriguing mitigation approach. Lastly, the obtained PIM cancellation is more effective for rusty MCS then for clean MCS. This is due to the rusty source producing a stronger third-order PIM interference that can be more efficiently suppressed, and due to the clean source having higher than third-order PIM components that leave more residual PIM. Measurements and Analysis 52

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4.5 Discussion

In this chapter, it is determined that PIM is indeed a significant problem in broadband radios as evidenced with the different measurements with different external PIM sources. Based on the previous research concerning external PIM, this chapter ought to produce more concrete results to contribute for the characterization of PIM generation from different external sources. The measurements and scenarios replicated emulate real cases of radio systems where PIM is likely. An analysis of PIM is made from both the transmitter side and the receiver side. From the transmitter side, the analysis is done based on the PIM power observed on each antenna element for the same configuration on the different sources. From the evaluation of the PSDs obtained, the distortion on one specific antenna element varies for different sources with the same configuration, e.g., the antenna element with worse or better PIM changes for different sources while maintaining the same configurations. From the receiver side, the analysis is done based on the PIM power observed on each antenna element for different configurations on the same source. From the analysis of the PSDs obtained, for the same source, the antenna element with worse or better PIM varies with the change in configurations. From these evaluations, it is derived that each external PIM source exhibits its own inherent characteristics, similar to an antenna. Furthermore, a conclusion regarding an optimal antenna polarization to receive less PIM, and an optimal amount of Tx, can not be made. However, as it was seen from observing the total PIM power varying over different measurements, this is due to the adoption of multicarrier signals with high PAPR. Lastly, we confirm that oxidation or corrosion increases the PIM power produced by the external source.

Regarding the mitigation aspect, we observe how a radio integrated algorithm performs. The results suggest that these types of algorithms can not fully mitigate the interference Measurements and Analysis 53 due to contributions from the residual power from the spectral regrowth. However, the data collected from the measurements can contribute to improve existing radio integrated mitigation techniques. For instance, it is evident from the measurements that different RX capture different PIM levels, and that different TXs contribute differently. Based on this, some algorithm based on supervised learning, e.g., Support Vector Machines (SVM), can be designed to determine the contributions of PIM from different Tx signals. Since PIM varies over time, an adaptive digital cancellation solution is called upon to also integrate existing radio systems.

Chapter 5

Conclusion and Future Work

This thesis addressed the PIM distortion problem in multiband radio systems. More specifically, characterizing the physics behind the triggering mechanisms that originate the nonlinear behavior in passive components, reviewing how the enhancement of radio systems (broadband radios) worsened the PIM problem and devised mitigation tech- niques, and, lastly, measurements analyzing the relation between external PIM power observed and BS antenna elements. The main purpose of this work was to complement the current knowledge on external PIM, hence some of the main findings are summarized below.

In the first part of this work, Chapter 2, we developed a mathematical approach to characterize the IMD imperfection and reviewed the nonlinear triggers of the two types of existing PIM sources, internal and external. More concretely, electron tunneling and ET conductivity for internal sources, and a PO approach to explain nonlinear current generation in metallic objects for external sources. Every situation where these mecha- nisms are prone to occur form a PIM transmitter. The appearance of these situations in radio systems is diversified as well as unpredictable and unavoidable, especially ag- ing and corrosion. Each PIM transmitter emits its own signal that gets accumulated throughout the transmission and can lead to interference in the Rx bands.

Next, in Chapter 3 we reviewed the enhancement of radio systems, particularly tech- niques embedded in the radios to increase data rates (CA), and enlarge the bandwidth. The devised broadband radio systems worsen the spectral regrowth, i.e., PIM’s effect in the network. The known mitigation techniques, physical and radio integrated, main strategy is either avoiding the nonlinear behavior of the passive components by under- taking physical endeavors towards so, or avoiding the IM spurious frequencies performing

55 Conclusion 56 frequency planning by relying on the mathematical model. We considered these insuffi- cient as modulated signals generate broader PIMP which makes PIM interference inex- orable. Adaptive PIM cancellation algorithms are surfacing as the next logical counter measure to the problem but they still need improvements for better performance.

In the final part of this work, Chapter 4, we presented the analysis of the measurements performed. By emulating a real scenario of a broadband radio system transmitting to- wards different PIM sources inside an anechoic chamber, we ought to investigate the relation between observed PIM power in the Rx and PIM source. The radio setup uti- lized comprised of a multicarrier LTE signal from Band2 transmitted from the antenna elements linearly polarized +45◦ and −45◦ installed on a high power BS. In addition, we tested three distinct sources that emulated likely cases of external PIM, steel wool, clean metal clamp support structure and rusty metal clamp support structure. In an initial observation of the PSDs, we were not able to assess a specific pattern common to each source, i.e., the PIM power observed in each antenna element would vary tremen- dously depending on the amount of Tx chosen for each source, hence a specific antenna polarization could not be said to be better or worse to receive the signal. In addition, in consecutive measurements, we denoted that the total PIM power observed on the Rx largely varies within a . This can be attributed to the possibility of generation of constructive or destructive interference in the source due to the use of multicarrier Tx signals. Lastly, we determined that each external PIM source can be viewed as a PIM antenna, with an unique radiation pattern depending on the conditions it is exposed to at the moment of the transmission. The directivity of PIM produced by each source varies spatially. Disturbances like change of height, direction, time when the measurement is taken or interaction with the source change the PIM power observed in each element drastically.

Overall, in this thesis, we have characterized the PIM distortion phenomenon in multi- band radio systems. The main outcome of this work are the measurements performed as the analysis provides valuable insight towards optimizing current mitigation techniques even though better characterization can be obtained through single-tones signals. As a result, several different research opportunities exist as a direct result of this work in ex- ternal PIM. For instance, further work would be to implement, in adaptive cancellation algorithms, features to accommodate the sudden changes in the PIM distortion values as well as a machine learning feature to optimize the total PIM power received in the BS. This would be done by selecting the most appropriate receivers, e.g., antenna element with lower PIM. Additionally, it is important to research how beamforming and massive MIMO could lower the PIM power received in a BS, i.e., improve the suppression of PIM. With beamforming, the remaining variables of the external PIM scenario such as, Conclusion 57 tilting and steering, whereas with massive MIMO, the number of antennas is incorpo- rated in the study. Finally, it would also be interesting to investigate a scenario where the source is transient and exposed to other environmental conditions. These form good topics for future work beyond this thesis.

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